generateMATLABFunction
Syntax
Description
Generate Equivalent MATLAB Function
generateMATLABFunction(
generates code
and opens an untitled file containing a function named
afe
)extractAudioFeatures
. The generated MATLAB® function has the
signature:
featureVector = extractAudioFeatures(audioIn)
featureVector = extract(afe,audioIn)
Generate MATLAB Function for Stream Processing
generateMATLABFunction(___,'IsStreaming',
specifies whether the function is intended for stream (single-frame) processing. If
TF
)TF
is specified as true
, the resulting function
requires single-frame input of length numel(afe.Window)
. If individual
feature extractors have state, the resulting function maintains the state between calls.
If unspecified, TF
defaults to false
. The streaming
function has the
signature:
featureVector = functionName(audioIn,varargin)
featureVector
depends on the value of
IsStreaming
.
If
IsStreaming
was set totrue
, thenfeatureVector
is returned as an M-by-N matrix, where M is the number of features extracted and N is the number of channels.If
IsStreaming
was set tofalse
, thenfeatureVector
is returned as an L-by-M-by-N array, where L is the number of hops, M is the number of feature vectors, and N is the number of channels.
The possible values of varargin
depends on the
configuration of your audioFeatureExtractor
object,
afe
.
If the features your
audioFeatureExtractor
object extracts do not require state, thenvarargin
must be empty.If the features your
audioFeatureExtractor
object extracts require state, thenvarargin
can be the optional name-value pair'Reset'
and eithertrue
orfalse
. If you call the function with'Reset'
set totrue
, then the function clears any state before calculating and returning the feature vector.
Examples
Generate Equivalent MATLAB® Function
You can use the audioFeatureExtractor
object while developing a feature extraction pipeline in MATLAB. Once you are ready to deploy your system to a device or integrate it into a larger system, use generateMATLABFunction
to create a MATLAB function suitable for C/C++ code generation. Then use MATLAB Coder™ to generate equivalent C/C++ code.
Read in an audio file. You will use this audio file to verify the equivalency of the audioFeatureExtractor
object and the generated MATLAB function.
[audioIn,fs] = audioread('Counting-16-44p1-mono-15secs.wav');
Create an audioFeatureExtractor
object to extract the Bark spectrum, the delta gammatone cepstral coefficients (GTCC), and the harmonic ratio.
afe = audioFeatureExtractor("Window",hann(512,"periodic"), ... "OverlapLength",256, ... "SampleRate",fs, ... "FFTLength",1024, ... 'barkSpectrum',true, ... "gtccDelta",true, ... "harmonicRatio",true)
afe = audioFeatureExtractor with properties: Properties Window: [512x1 double] OverlapLength: 256 SampleRate: 44100 FFTLength: 1024 SpectralDescriptorInput: 'linearSpectrum' FeatureVectorLength: 46 Enabled Features barkSpectrum, gtccDelta, harmonicRatio Disabled Features linearSpectrum, melSpectrum, erbSpectrum, mfcc, mfccDelta, mfccDeltaDelta gtcc, gtccDeltaDelta, spectralCentroid, spectralCrest, spectralDecrease, spectralEntropy spectralFlatness, spectralFlux, spectralKurtosis, spectralRolloffPoint, spectralSkewness, spectralSlope spectralSpread, pitch, zerocrossrate, shortTimeEnergy To extract a feature, set the corresponding property to true. For example, obj.mfcc = true, adds mfcc to the list of enabled features.
Call generateMATLABFunction
on the object and specify a name for the generated MATLAB function.
functionName = 'extractAudioFeatures';
generateMATLABFunction(afe,functionName)
The generated function is saved to your current folder.
type extractAudioFeatures
function featureVector = extractAudioFeatures(x) %extractAudioFeatures Extract multiple features from batch audio % featureVector = extractAudioFeatures(audioIn) returns audio features % extracted from audioIn. % % Parameters of the audioFeatureExtractor used to generate this % function must be honored when calling this function. % - Sample rate of the input should be 44100 Hz. % - Input frame length should be greater than or equal to 512 samples. % % % % Example 1: Extract features % source = dsp.ColoredNoise(SamplesPerFrame=44100); % for ii = 1:10 % audioIn = source(); % featureArray = extractAudioFeatures(audioIn); % % ... do something with featureArray ... % end % % % % Example 2: Generate code % targetDataType = "single"; % codegen extractAudioFeatures -args {ones(44100,1,targetDataType)} % source = dsp.ColoredNoise(SamplesPerFrame=44100, ... % OutputDataType=targetDataType); % for ii = 1:10 % audioIn = source(); % featureArray = extractAudioFeatures_mex(audioIn); % % ... do something with featureArray ... % end % % See also audioFeatureExtractor, dsp.AsyncBuffer, codegen. % Generated by audioFeatureExtractor on 20-Jul-2024 19:09:56 UTC-04:00 %#codegen dataType = underlyingType(x); [numSamples,numChannels] = size(x); props = coder.const(getProps(dataType)); persistent config outputIndex if isempty(outputIndex) [config, outputIndex] = coder.const(@getConfig,dataType,props); end % Preallocate feature vector numHops = floor((numSamples-numel(props.Window))/(numel(props.Window) - props.OverlapLength)) + 1; featureVector = coder.nullcopy(zeros(numHops,props.NumFeatures,numChannels,dataType)); % Short-time Fourier transform Y = stft(x,Window=props.Window,OverlapLength=props.OverlapLength,FFTLength=props.FFTLength,FrequencyRange="onesided"); Z = reshape(Y,[],numHops*numChannels); Zpower = real(Z.*conj(Z)); % Bark spectrum y = applyFilterBank(config.barkSpectrum.FilterBank,Zpower,dataType); barkSpectrum = reshape(y,[],numHops,numChannels); featureVector(:,outputIndex.barkSpectrum,:) = permute(barkSpectrum,[2,1,3]); % ERB spectrum y = applyFilterBank(config.erbSpectrum.FilterBank,Zpower,dataType); erbSpectrum = reshape(y,[],numHops,numChannels); % Gammatone-frequency cepstral coefficients (GTCC) gammacc = cepstralCoefficients(erbSpectrum,NumCoeffs=13,Rectification="log"); featureVector(:,outputIndex.gtccDelta,:) = audioDelta(gammacc,9); % Periodicity features featureVector(:,outputIndex.harmonicRatio,:) = harmonicRatio(x,props.SampleRate,Window=props.Window,OverlapLength=props.OverlapLength); end function props = getProps(dataType) props.Window = cast([0;3.764908042774850471801073581446e-05;0.00015059065189787501637397326703649;0.00033880770582522812262027400720399;0.00060227189741379749676752908271737;0.00094094354992541040516584871511441;0.0013547716606548965145861984638032;0.0018436939086109993546358509775018;0.0024076366639015356341246842930559;0.0030465149988219697441138578142272;0.0037602327006450164681439218838932;0.0045486822861099951431640420196345;0.0054117450176094927805081624683226;0.0063492909210707826339614712196635;0.0073611788055293891908092973608291;0.0084472562843918574948531841073418;0.0096073597983847847103788808453828;0.010841314640186172635338834879803;0.012148934980735714983524076160393;0.0135300238972199116105343819072;0.014984373402728012880658070571371;0.016511764477573964704504305700539;0.018111967102280079888743102856097;0.019784740292217106727434838830959;0.021529832133895587809035987447714;0.023346979822903068946260418670136;0.025235909703481662624824366503162;0.027196337309739360144078545999946;0.029227967408489596845555524851079;0.031330494043712520113587061132421;0.0335036005826305216537264186627;0.035746959763392205378096377899055;0.038060233744356630758431947469944;0.040443074154971114797518794148345;0.042895122148234654524401321395999;0.045416008454738809874129401578102;0.048005353438278330902022617010516;0.050662767153023091637464858649764;0.053387849402242337770729818657856;0.056180189798573032522455150683527;0.059039367825822475221997365224524;0.061964952902296699388529077623389;0.064956504445644269729598363483092;0.068013571939206651784104451508028;0.071135694999863940957141039689304;0.07432240344736740222941762112896;0.077573217375146441554534249007702;0.080887647222580960626459045670344;0.084265193848727382164298660427448;0.087705348607487354506417887023417;0.091207593424208144305964651721297;0.094771400873702615896831957797986;0.098396234259677528566356841110974;0.1020815476955582168372416163038;0.10582678618669683068276299309218;0.10963138571395275588926665477629;0.11349477331863150331159317829588;0.11741636718877052070197919420025;0.12139557674675771625771858452936;0.12543180273827031490085914811061;0.12952443732252039154673184384592;0.13367286416379359215156341633701;0.1378764585242664986175498142984;0.14213458735809070265787568132509;0.14644660940672621363134453531529;0.1508118752955135422055832350452;0.15522972763146652974697303761786;0.159699501102273433428280213775;0.16422052257649077944279270013794;0.16879211120491410813571064863936;0.17341357852311156673152936491533;0.17808422855510425142355757088808;0.18280335791817725610286515802727;0.1875702559288067727827353792236;0.19238420470968659037325210192648;0.19724447929783722743835028268222;0.20215034775378326603600953603745;0.2071010712717805679616844827251;0.21209590429107733067226604362077;0.21713409460819338425707769602013;0.22221488349019885566448806457629;0.22733750578897676808409755722096;0.23250119005645136782689519350242;0.23770515866076558086916747924988;0.24294862790338916935795054996561;0.248230808137141212288412361886;0.25355090388510792553944384053466;0.25890811396043855729942606558325;0.26430163158700109571341840819514;0.2697306445208800251833736183471;0.27519433517269670241844892188965;0.28069188073073614297925360006047;0.28622245328485890203396024844551;0.29178521995118134046975910678157;0.29737934299750506950132944439247;0.3030039799694759228287921359879;0.30865828381745508135480804412509;0.31434140302408120071220309910132;0.32005248173250588905602853628807;0.32579065987528277315021796312067;0.33155507330389000220094430915196;0.33734485391886848137943388792337;0.34315912980055418568525738010067;0.34899702534038590240328403524472;0.354857661372768862229065689462;0.36074015530747349789209010850755;0.36664362126255078955239241622621;0.37256717019774265864384688029531;0.37850991004836798126120811502915;0.38447094585966434809876091094338;0.39044937992156514283692558819894;0.39644431190389073371704853343545;0.40245483899193584820253022371617;0.40848005602242948297586622175004;0.41451905561984930814745098359708;0.42057092833306930490522290710942;0.42663476277231915378962412432884;0.43270964574643688838051502898452;0.43879466240039188829058502960834;0.44488889635305839398426996922353;0.45099142983521961491888419004681;0.4571013438277800600140210462996;0.46321771820016627296823230608425;0.46933963184889565534163580196036;0.47546616283629095089935390205937;0.481596388529320518223642011435;0.48772938573854385246875153825385;0.49386423085714004077573235917953;0.49999999999999994448884876874217;0.50613576914285995922426764082047;0.51227061426145603650894599923049;0.518403611470679481776357988565;0.52453383716370904910064609794063;0.53066036815110428914721296678181;0.53678228179983367152061646265793;0.54289865617221988447482772244257;0.54900857016478032956996457869536;0.55511110364694149499342756826081;0.56120533759960811170941497039166;0.56729035425356300059718250849983;0.57336523722768084621037587567116;0.57942907166693058407247463037493;0.58548094438015063634139778514509;0.59151994397757046151298254699213;0.59754516100806409628631854502601;0.60355568809610926628295146656455;0.60955062007843485716307441180106;0.61552905414033554087893662654096;0.6214900899516319077164894224552;0.62743282980225723033385065718903;0.63335637873744921044760758377379;0.63925984469252650210790989149245;0.64514233862723102674863184802234;0.65100297465961398657441350223962;0.65684087019944570329244015738368;0.66265514608113140759826364956098;0.66844492669610999779905569084804;0.67420934012471722684978203687933;0.67994751826749411094397146371193;0.68565859697591879928779690089868;0.69134171618254480762288949335925;0.69699602003052396614890540149645;0.70262065700249487498751932434971;0.70821478004881854850793843070278;0.71377754671514093143258605778101;0.71930811926926363497614147490822;0.72480566482730335309270230936818;0.73026935547912008583892884416855;0.73569836841299884877543036054703;0.7410918860395613316782714719011;0.74644909611489196343825369694969;0.75176919186285873220043640685617;0.75705137209661077513089821877657;0.76229484133923430810853005823446;0.7674988099435484656396511127241;0.77266249421102317640475121152122;0.77778511650980097780205824165023;0.78286590539180656023177107272204;0.78790409570892272483888518763706;0.7928989287282194320383155172749;0.79784965224621662294168800144689;0.80275552070216271705049848605995;0.80761579529031335411559666681569;0.81242974407119317170611338951858;0.81719664208182263287483237945708;0.82191577144489569306529119785409;0.82658642147688832224616817256901;0.83120788879508600288659181387629;0.83577947742350922055720729986206;0.84030049889772651106056855496718;0.84477027236853352576417819363996;0.84918812470448634677211430243915;0.85355339059327373085750423342688;0.85786541264190929734212431867491;0.86212354147573333484899649192812;0.86632713583620635233728535240516;0.87047556267747938640866323112277;0.87456819726172962958798962063156;0.8786044232532423947645838779863;0.88258363281122953480917203705758;0.88650522668136844117725559044629;0.89036861428604718859958211396588;0.89417321381330316931723700690782;0.89791845230444167214045592118055;0.9016037657403224159224919276312;0.90522859912629738410316804220201;0.90879240657579174467173288576305;0.91229465139251253447127965046093;0.91573480615127267334685257083038;0.91911235277741898386238972307183;0.9224267826248535584454657509923;0.92567759655263259777058237887104;0.92886430500013594802055649779504;0.93198642806079334821589554849197;0.93504349555435561924809917400125;0.93803504709770324510031969111878;0.94096063217417746926685140351765;0.94381981020142691196639361805865;0.94661215059775760671811895008432;0.94933723284697690836253514135024;0.95199464656172172460912861424731;0.9545839915452611901258705984219;0.957104877851765345475598678604;0.95955692584502894071363243710948;0.96193976625564336924156805253006;0.96425304023660773911075239084312;0.96649639941736942283512235007947;0.96866950595628742437526170760975;0.97077203259151034764329324389109;0.9728036626902605288336189914844;0.97476409029651833737517563349684;0.97665302017709687554258835007204;0.97847016786610441219096401255229;0.98021525970778289327256516116904;0.98188803289771997562240812840173;0.98348823552242603529549569429946;0.98501562659727204263049316068646;0.98646997610277997736716315557715;0.98785106501926422950532469258178;0.98915868535981377185350993386237;0.99039264020161521528962111915462;0.99155274371560819801629804715049;0.99263882119447055529803947138134;0.99365070907892916185488729752251;0.9945882549823905627306430687895;0.99545131771388994934568472672254;0.99623976729935503904300730937393;0.9969534850011780857670373734436;0.99759236333609835334357285319129;0.99815630609138894513421291776467;0.9986452283393451034854138015362;0.99905905645007453408368292002706;0.99939772810258620250323247091728;0.99966119229417471636622849473497;0.99984940934810206947247479547514;0.99996235091957230700643322052201;1;0.99996235091957230700643322052201;0.99984940934810206947247479547514;0.99966119229417471636622849473497;0.99939772810258620250323247091728;0.99905905645007453408368292002706;0.9986452283393451034854138015362;0.99815630609138894513421291776467;0.99759236333609835334357285319129;0.9969534850011780857670373734436;0.99623976729935503904300730937393;0.99545131771388994934568472672254;0.9945882549823905627306430687895;0.99365070907892916185488729752251;0.99263882119447055529803947138134;0.99155274371560819801629804715049;0.99039264020161521528962111915462;0.98915868535981377185350993386237;0.98785106501926422950532469258178;0.98646997610277997736716315557715;0.98501562659727204263049316068646;0.98348823552242603529549569429946;0.98188803289771997562240812840173;0.98021525970778289327256516116904;0.97847016786610441219096401255229;0.97665302017709687554258835007204;0.97476409029651833737517563349684;0.9728036626902605288336189914844;0.97077203259151034764329324389109;0.96866950595628742437526170760975;0.96649639941736942283512235007947;0.96425304023660773911075239084312;0.96193976625564336924156805253006;0.95955692584502894071363243710948;0.957104877851765345475598678604;0.9545839915452611901258705984219;0.95199464656172172460912861424731;0.94933723284697690836253514135024;0.94661215059775760671811895008432;0.94381981020142691196639361805865;0.94096063217417746926685140351765;0.93803504709770324510031969111878;0.93504349555435561924809917400125;0.93198642806079334821589554849197;0.92886430500013594802055649779504;0.92567759655263259777058237887104;0.9224267826248535584454657509923;0.91911235277741898386238972307183;0.91573480615127267334685257083038;0.91229465139251253447127965046093;0.90879240657579174467173288576305;0.90522859912629738410316804220201;0.9016037657403224159224919276312;0.89791845230444167214045592118055;0.89417321381330316931723700690782;0.89036861428604718859958211396588;0.88650522668136844117725559044629;0.88258363281122953480917203705758;0.8786044232532423947645838779863;0.87456819726172962958798962063156;0.87047556267747938640866323112277;0.86632713583620635233728535240516;0.86212354147573333484899649192812;0.85786541264190929734212431867491;0.85355339059327373085750423342688;0.84918812470448634677211430243915;0.84477027236853352576417819363996;0.84030049889772651106056855496718;0.83577947742350922055720729986206;0.83120788879508600288659181387629;0.82658642147688832224616817256901;0.82191577144489569306529119785409;0.81719664208182263287483237945708;0.81242974407119317170611338951858;0.80761579529031335411559666681569;0.80275552070216271705049848605995;0.79784965224621662294168800144689;0.7928989287282194320383155172749;0.78790409570892272483888518763706;0.78286590539180656023177107272204;0.77778511650980097780205824165023;0.77266249421102317640475121152122;0.7674988099435484656396511127241;0.76229484133923430810853005823446;0.75705137209661077513089821877657;0.75176919186285873220043640685617;0.74644909611489196343825369694969;0.7410918860395613316782714719011;0.73569836841299884877543036054703;0.73026935547912008583892884416855;0.72480566482730335309270230936818;0.71930811926926363497614147490822;0.71377754671514093143258605778101;0.70821478004881854850793843070278;0.70262065700249487498751932434971;0.69699602003052396614890540149645;0.69134171618254480762288949335925;0.68565859697591879928779690089868;0.67994751826749411094397146371193;0.67420934012471722684978203687933;0.66844492669610999779905569084804;0.66265514608113140759826364956098;0.65684087019944570329244015738368;0.65100297465961398657441350223962;0.64514233862723102674863184802234;0.63925984469252650210790989149245;0.63335637873744921044760758377379;0.62743282980225723033385065718903;0.6214900899516319077164894224552;0.61552905414033554087893662654096;0.60955062007843485716307441180106;0.60355568809610926628295146656455;0.59754516100806409628631854502601;0.59151994397757046151298254699213;0.58548094438015063634139778514509;0.57942907166693058407247463037493;0.57336523722768084621037587567116;0.56729035425356300059718250849983;0.56120533759960811170941497039166;0.55511110364694149499342756826081;0.54900857016478032956996457869536;0.54289865617221988447482772244257;0.53678228179983367152061646265793;0.53066036815110428914721296678181;0.52453383716370904910064609794063;0.518403611470679481776357988565;0.51227061426145603650894599923049;0.50613576914285995922426764082047;0.49999999999999994448884876874217;0.49386423085714004077573235917953;0.48772938573854385246875153825385;0.481596388529320518223642011435;0.47546616283629095089935390205937;0.46933963184889565534163580196036;0.46321771820016627296823230608425;0.4571013438277800600140210462996;0.45099142983521961491888419004681;0.44488889635305839398426996922353;0.43879466240039188829058502960834;0.43270964574643688838051502898452;0.42663476277231915378962412432884;0.42057092833306930490522290710942;0.41451905561984930814745098359708;0.40848005602242948297586622175004;0.40245483899193584820253022371617;0.39644431190389073371704853343545;0.39044937992156514283692558819894;0.38447094585966434809876091094338;0.37850991004836798126120811502915;0.37256717019774265864384688029531;0.36664362126255078955239241622621;0.36074015530747349789209010850755;0.354857661372768862229065689462;0.34899702534038590240328403524472;0.34315912980055418568525738010067;0.33734485391886848137943388792337;0.33155507330389000220094430915196;0.32579065987528277315021796312067;0.32005248173250588905602853628807;0.31434140302408120071220309910132;0.30865828381745508135480804412509;0.3030039799694759228287921359879;0.29737934299750506950132944439247;0.29178521995118134046975910678157;0.28622245328485890203396024844551;0.28069188073073614297925360006047;0.27519433517269670241844892188965;0.2697306445208800251833736183471;0.26430163158700109571341840819514;0.25890811396043855729942606558325;0.25355090388510792553944384053466;0.248230808137141212288412361886;0.24294862790338916935795054996561;0.23770515866076558086916747924988;0.23250119005645136782689519350242;0.22733750578897676808409755722096;0.22221488349019885566448806457629;0.21713409460819338425707769602013;0.21209590429107733067226604362077;0.2071010712717805679616844827251;0.20215034775378326603600953603745;0.19724447929783722743835028268222;0.19238420470968659037325210192648;0.1875702559288067727827353792236;0.18280335791817725610286515802727;0.17808422855510425142355757088808;0.17341357852311156673152936491533;0.16879211120491410813571064863936;0.16422052257649077944279270013794;0.159699501102273433428280213775;0.15522972763146652974697303761786;0.1508118752955135422055832350452;0.14644660940672621363134453531529;0.14213458735809070265787568132509;0.1378764585242664986175498142984;0.13367286416379359215156341633701;0.12952443732252039154673184384592;0.12543180273827031490085914811061;0.12139557674675771625771858452936;0.11741636718877052070197919420025;0.11349477331863150331159317829588;0.10963138571395275588926665477629;0.10582678618669683068276299309218;0.1020815476955582168372416163038;0.098396234259677528566356841110974;0.094771400873702615896831957797986;0.091207593424208144305964651721297;0.087705348607487354506417887023417;0.084265193848727382164298660427448;0.080887647222580960626459045670344;0.077573217375146441554534249007702;0.07432240344736740222941762112896;0.071135694999863940957141039689304;0.068013571939206651784104451508028;0.064956504445644269729598363483092;0.061964952902296699388529077623389;0.059039367825822475221997365224524;0.056180189798573032522455150683527;0.053387849402242337770729818657856;0.050662767153023091637464858649764;0.048005353438278330902022617010516;0.045416008454738809874129401578102;0.042895122148234654524401321395999;0.040443074154971114797518794148345;0.038060233744356630758431947469944;0.035746959763392205378096377899055;0.0335036005826305216537264186627;0.031330494043712520113587061132421;0.029227967408489596845555524851079;0.027196337309739360144078545999946;0.025235909703481662624824366503162;0.023346979822903068946260418670136;0.021529832133895587809035987447714;0.019784740292217106727434838830959;0.018111967102280079888743102856097;0.016511764477573964704504305700539;0.014984373402728012880658070571371;0.0135300238972199116105343819072;0.012148934980735714983524076160393;0.010841314640186172635338834879803;0.0096073597983847847103788808453828;0.0084472562843918574948531841073418;0.0073611788055293891908092973608291;0.0063492909210707826339614712196635;0.0054117450176094927805081624683226;0.0045486822861099951431640420196345;0.0037602327006450164681439218838932;0.0030465149988219697441138578142272;0.0024076366639015356341246842930559;0.0018436939086109993546358509775018;0.0013547716606548965145861984638032;0.00094094354992541040516584871511441;0.00060227189741379749676752908271737;0.00033880770582522812262027400720399;0.00015059065189787501637397326703649;3.764908042774850471801073581446e-05],dataType);props.OverlapLength = cast(256,dataType); props.SampleRate = cast(44100,dataType); props.FFTLength = uint16(1024); props.NumFeatures = uint8(46); end function [config, outputIndex] = getConfig(dataType, props) powerNormalizationFactor = 1/(sum(props.Window)^2); barkFilterbank = designAuditoryFilterBank(props.SampleRate, ... FrequencyScale="bark", ... FFTLength=props.FFTLength, ... OneSided=true, ... FrequencyRange=[0 22050], ... NumBands=32, ... Normalization="bandwidth", ... FilterBankDesignDomain="linear"); barkFilterbank = barkFilterbank*powerNormalizationFactor; config.barkSpectrum.FilterBank = cast(barkFilterbank,dataType); erbFilterbank = coder.const(@feval,'designAuditoryFilterBank',props.SampleRate, ... FrequencyScale="erb", ... FFTLength=props.FFTLength, ... OneSided=true, ... FrequencyRange=[0 22050], ... NumBands=43, ... Normalization="bandwidth"); erbFilterbank = erbFilterbank*powerNormalizationFactor; config.erbSpectrum.FilterBank = cast(erbFilterbank,dataType); outputIndex.barkSpectrum = uint8(1:32); outputIndex.gtccDelta = uint8(33:45); outputIndex.harmonicRatio = uint8(46); end function y = applyFilterBank(filterBank, Z, dataType, varargin) if isempty(coder.target) y = filterBank*Z; else % Generate optimized C/C++ code for filter bank operation [numBands,filterLength] = size(filterBank); numChan = size(Z,2); if nargin == 3 y = zeros(numBands,numChan,dataType); else y = varargin{1}; end for channel = 1:numChan temp = zeros(numBands,1,dataType); for jj = 1:filterLength temp = temp + Z(jj,channel)*filterBank(:,jj); end y(:,channel) = temp; end end end
Calling the generated function is equivalent to calling extract
on the audioFeatureExtrator
object. You can replace calls to extract
with calls to the generated function in your code. Verify the equivalency between the object and the function.
a = extract(afe,audioIn); b = extractAudioFeatures(audioIn); isequal(a,b)
ans = logical
1
The generated function contains help text that indicates any requirements on the input. In this example, the only requirement is that the input sample rate should be 44.1 kHz. The help text also contains custom examples. These examples show how to use the function directly in MATLAB and how to generate C/C++ code.
help extractAudioFeatures
extractAudioFeatures Extract multiple features from batch audio featureVector = extractAudioFeatures(audioIn) returns audio features extracted from audioIn. Parameters of the audioFeatureExtractor used to generate this function must be honored when calling this function. - Sample rate of the input should be 44100 Hz. - Input frame length should be greater than or equal to 512 samples. % Example 1: Extract features source = dsp.ColoredNoise(SamplesPerFrame=44100); for ii = 1:10 audioIn = source(); featureArray = extractAudioFeatures(audioIn); % ... do something with featureArray ... end % Example 2: Generate code targetDataType = "single"; codegen extractAudioFeatures -args {ones(44100,1,targetDataType)} source = dsp.ColoredNoise(SamplesPerFrame=44100, ... OutputDataType=targetDataType); for ii = 1:10 audioIn = source(); featureArray = extractAudioFeatures_mex(audioIn); % ... do something with featureArray ... end See also audioFeatureExtractor, dsp.AsyncBuffer, codegen.
Run the first example to see how to use the function to extract features in MATLAB.
source = dsp.ColoredNoise("SamplesPerFrame",44100); for ii = 1:10 audioIn = source(); featureArray = extractAudioFeatures(audioIn); % ... do something with featureArray ... end
Run the second example to see how to generate a MATLAB executable from the function. Then use the MEX file to extract features while working in MATLAB. MATLAB Coder™ is required to run the following code.
targetDataType = "single"; codegen extractAudioFeatures -args {ones(44100,1,targetDataType)}
Code generation successful.
source = dsp.ColoredNoise("SamplesPerFrame",44100, ... "OutputDataType",targetDataType); for ii = 1:10 audioIn = source(); featureArray = extractAudioFeatures_mex(audioIn); % ... do something with featureArray ... end
Generate MATLAB® Function for Stream Processing
You can use the audioFeatureExtractor
object to develop a feature extraction pipeline in MATLAB. The audioFeatureExtractor
is optimized to extract features from audio signals that contain several windows of data. Typically, audio features are extracted on time scales from 5 ms to 100 ms, depending on the application. When you are ready to deploy your system to a device or to integrate it into a larger system, you can use generateMATLABFunction
to create a MATLAB function suitable for C/C++ code generation. Deployed systems are often concerned with minimizing latency. You can set the IsStreaming
parameter to true
when calling generateMATLABFunction
to generate a MATLAB function that is optimized for stream processing. The generated MATLAB function assumes that the input has already been buffered and requires a fixed input frame size. The generated MATLAB function also maintains any required state for you between calls.
Read in an audio file. You will use this audio file to verify the approximate equivalency of the audioFeatureExtractor
object and the generated MATLAB function.
[audioToVerify,fs] = audioread('Counting-16-44p1-mono-15secs.wav');
Create an audioFeatureExtractor
object to extract the mel frequency cepstral coefficients (MFCC), the delta and delta-delta MFCC, the spectral centroid, and the pitch. Extract features from 30 ms windows with 20 ms overlap between windows.
afe = audioFeatureExtractor("Window",hann(round(0.03*fs),'periodic'), ... "OverlapLength",round(0.02*fs), ... "SampleRate",fs, ... "mfcc",true, ... "mfccDelta",true, ... "mfccDeltaDelta",true, ... "spectralCentroid",true, ... "pitch",true)
afe = audioFeatureExtractor with properties: Properties Window: [1323x1 double] OverlapLength: 882 SampleRate: 44100 FFTLength: [] SpectralDescriptorInput: 'linearSpectrum' FeatureVectorLength: 41 Enabled Features mfcc, mfccDelta, mfccDeltaDelta, spectralCentroid, pitch Disabled Features linearSpectrum, melSpectrum, barkSpectrum, erbSpectrum, gtcc, gtccDelta gtccDeltaDelta, spectralCrest, spectralDecrease, spectralEntropy, spectralFlatness, spectralFlux spectralKurtosis, spectralRolloffPoint, spectralSkewness, spectralSlope, spectralSpread, harmonicRatio zerocrossrate, shortTimeEnergy To extract a feature, set the corresponding property to true. For example, obj.mfcc = true, adds mfcc to the list of enabled features.
Call generateMATLABFunction
on the object and specify a name and the full path for the generated MATLAB function. Set IsStreaming
to true
to generate a MATLAB function optimized for stream processing.
filename = fullfile(tempdir,"extractAudioFeatures"); generateMATLABFunction(afe,filename,'IsStreaming',true);
The generated function is saved to the tempdir
folder. Because the mfccDelta
and mfccDeltaDelta
features require state, the generated function includes the ability to reset states using the optional name-value pair "Reset"
and either true
or false
. If you generate a function that does not require state, the "Reset"
parameter is not included in the generated function.
cd(tempdir)
type extractAudioFeatures
function featureVector = extractAudioFeatures(x, varargin) %extractAudioFeatures Extract multiple features from streaming audio % featureVector = extractAudioFeatures(audioIn) returns audio features % extracted from audioIn. % % featureVector = extractAudioFeatures(audioIn,Reset=TF) returns feature extractors % to their initial conditions before extracting features. % % Parameters of the audioFeatureExtractor used to generate this % function must be honored when calling this function. % - Sample rate of the input should be 44100 Hz. % - Frame length of the input should be 1323 samples. % - Successive frames of the input should be overlapped by % 882 samples before calling extractAudioFeatures. % % % % Example 1: Extract features % source = dsp.ColoredNoise(); % inputBuffer = dsp.AsyncBuffer; % for ii = 1:10 % audioIn = source(); % write(inputBuffer,audioIn); % while inputBuffer.NumUnreadSamples > 441 % x = read(inputBuffer,1323,882); % featureVector = extractAudioFeatures(x); % % ... do something with featureVector ... % end % end % % % % Example 2: Extract features from speech regions only % [audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav"); % audioIn = resample(audioIn,44100,fs); % source = dsp.AsyncBuffer(size(audioIn,1)); % write(source,audioIn); % TF = false; % while source.NumUnreadSamples > 441 % x = read(source,1323,882); % isSilence = var(x) < 0.01; % if ~isSilence % featureVector = extractAudioFeatures(x,Reset=TF); % TF = false; % else % TF = true; % end % % ... do something with featureVector ... % end % % % % Example 3: Generate code that does not use reset % targetDataType = "single"; % codegen extractAudioFeatures -args {ones(1323,1,targetDataType)} % source = dsp.ColoredNoise(OutputDataType=targetDataType); % inputBuffer = dsp.AsyncBuffer; % for ii = 1:10 % audioIn = source(); % write(inputBuffer,audioIn); % while inputBuffer.NumUnreadSamples > 441 % x = read(inputBuffer,1323,882); % featureVector = extractAudioFeatures_mex(x); % % ... do something with featureVector ... % end % end % % % % Example 4: Generate code that uses reset % targetDataType = "single"; % codegen extractAudioFeatures -args {ones(1323,1,targetDataType),"Reset",true} % [audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav"); % audioIn = resample(audioIn,44100,fs); % source = dsp.AsyncBuffer(size(audioIn,1)); % write(source,cast(audioIn,targetDataType)); % TF = false; % while source.NumUnreadSamples > 441 % x = read(source,1323,882); % isSilence = var(x) < 0.01; % if ~isSilence % featureVector = extractAudioFeatures_mex(x,Reset=TF); % TF = false; % else % TF = true; % end % % ... do something with featureVector ... % end % % See also audioFeatureExtractor, dsp.AsyncBuffer, codegen. % Generated by audioFeatureExtractor on 20-Jul-2024 19:10:38 UTC-04:00 %#codegen dataType = underlyingType(x); numChannels = size(x,2); props = coder.const(getProps(dataType)); persistent config outputIndex state if isempty(outputIndex) [config, outputIndex] = coder.const(@getConfig,dataType,props); state = getState(dataType,numChannels); else assert(state.NumChannels == numChannels) end if nargin==3 if strcmpi(varargin{1},"Reset") && varargin{2} state = reset(state); end end % Preallocate feature vector featureVector = coder.nullcopy(zeros(props.NumFeatures,numChannels,dataType)); % Fourier transform Y = fft(bsxfun(@times,x,props.Window),props.FFTLength); Z = Y(config.OneSidedSpectrumBins,:); Zpower = real(Z.*conj(Z)); % Linear spectrum linearSpectrum = Zpower(config.linearSpectrum.FrequencyBins,:)*config.linearSpectrum.NormalizationFactor; linearSpectrum(1,:) = 0.5*linearSpectrum(1,:); linearSpectrum = reshape(linearSpectrum,[],1,numChannels); % Mel spectrum y = applyFilterBank(config.melSpectrum.FilterBank,Zpower,dataType); melSpectrum = reshape(y,[],1,numChannels); % Mel-frequency cepstral coefficients (MFCC) melcc = cepstralCoefficients(melSpectrum,NumCoeffs=13,Rectification="log"); featureVector(outputIndex.mfcc,:) = melcc; [melccDelta,state.mfccDelta] = audioDelta(melcc,9,state.mfccDelta); featureVector(outputIndex.mfccDelta,:) = melccDelta; [featureVector(outputIndex.mfccDeltaDelta,:),state.mfccDeltaDelta] = audioDelta(melccDelta,9,state.mfccDeltaDelta); % Spectral descriptors featureVector(outputIndex.spectralCentroid,:) = spectralCentroid(linearSpectrum,config.SpectralDescriptorInput.FrequencyVector); % Periodicity features featureVector(outputIndex.pitch,:) = pitch(x,props.SampleRate,WindowLength=numel(props.Window),OverlapLength=props.OverlapLength,Method='NCF',Range=coder.const(cast([50 400],like=x))); end function props = getProps(dataType) props.Window = cast([0;5.6387032669191761158344888826832e-06;2.2554685887743453065468202112243e-05;5.0747566325726189973011059919372e-05;9.0216708695634029169241330237128e-05;0.00014096122277840184011665769503452;0.00020297996404095020039903829456307;0.00027627153366222012564890064822976;0.00036083427856448135884193106903695;0.00045666629145085790852931495464873;0.00056376541084829367989073034550529;0.00068212922115606922091046726563945;0.00081175505270059122864267919794656;0.00095263998179551112599483531084843;0.0011047808308075057759367609833134;0.001268174168228275444647579206503;0.00144281630875153776827346518985;0.0016287033133565165243794581328984;0.0018258309893965374293145487172296;0.00203419489069373016221220495936;0.0022537903176392259929627925885143;0.0024846123172992951033677400118904;0.0027266556835268129788119040313177;0.0029799149570789440488738364365418;0.0032443844257400433761517888342496;0.0035200581244507755940276183537208;0.0038069298354423408703439690725645;0.0041049930883769181200193543190835;0.0044142411604936038216351334995124;0.0047346670767599019491456147079589;0.0050662636100292091079211331816623;0.0054090232812036287413093305076472;0.0057629383594029470749831034481758;0.0061280008621386050648993659706321;0.0065042025554942206611030997009948;0.0068915349543108850305372925504344;0.0072899893223787315399420094763627;0.0076995566726339448315741265105316;0.008120227767361598569806346858968;0.0085519931184036557247907239798224;0.0089948429873734636608162418269785;0.0094487673858749121613698207511334;0.009913756075728086258891380566638;0.010389798569200026090442179338424;0.010876884129241204401949971725116;0.011375001769727999256787143167458;0.01188414025570999621450596350769;0.012404288103663951847721591548179;0.012935433581752309173396042751847;0.01347756471008809686651375159272;0.014030669261005046521972872142214;0.01459473475933348307620462946943;0.015169748482681433277008409277187;0.015755697461721951402324748414685;0.016352568480485274449165444821119;0.016960348076657194571481568345916;0.017579022541882538543944747289061;0.018208577922074309363154043239774;0.018849000017728712030873339244863;0.019500274384245008807425847408012;0.02016238633225159171402651736571;0.020835320927937328594481414256734;0.021519062993388182736254066185211;0.022213597106929605651259862497682;0.022918907603474591994086040358525;0.02363497857487673048382248452981;0.024361793870289027985620577965165;0.02509933709652845124082887195982;0.025847591618445353578437106989441;0.026606540559298896830853209394263;0.027376166801137580275593563783332;0.028156452985185376203247642479255;0.028947381512233305578263298230013;0.029748934543036231747947795156506;0.030561093998715427311196890514111;0.031383841561166136990834729658673;0.032217158673470969176833023084328;0.033061026540318172450838574150112;0.0339154261284257407815800888784;0.034780338166970736768490723989089;0.035655743148023777422395141911693;0.036541621326989126572470922837965;0.037437952723050060832576946268091;0.038344717119619620149251204566099;0.039261894064796187819865735946223;0.040189462871825232248568227078067;0.041127402619565822661229503864888;0.042075692152962140824001835426316;0.043034310083521154499663907699869;0.044003234789794509751459372637328;0.044982444417866696007024529535556;0.045971916881847485480960813220008;0.046971629864370534335193951847032;0.04798156081709631370912916281668;0.049001686961220980442988093273016;0.050031985287990077271302880035364;0.051072432559217451064625947765308;0.052123005307809389119455545369419;0.053183679838293862474074558122084;0.054254432227355209317209983055363;0.055335238324373370311093367490685;0.056426073751968952585400529642357;0.057526913906552734623289779847255;0.058637733958880777773714498835034;0.059758508854614589278497760460596;0.060889213314885726191505455062725;0.062029821836866561035606082441518;0.063180308694345155284821657915018;0.064340647938305295383543125353754;0.065510813397512468458927514802781;0.066690778679103335235822669346817;0.067880517169181586734083566625486;0.06908000203341801981338221594342;0.070289206217655719743930831100442;0.071508102448520238780815816426184;0.072736663234035159320001184823923;0.073974860864241431812615701346658;0.075222667411823096461631621423294;0.076480054732736613143373460843577;0.077746994466846075511057279072702;0.079023458038562588434672306902939;0.080309416657488919000229543598834;0.081604841319068810445713779699872;0.082909702805241181078343970511924;0.084223971685099041639688266513986;0.085547618315553630718994782000664;0.086880612842002546969411014288198;0.088222925199003432439326388703194;0.089574525110952041284662072939682;0.090935382092764971417864217073657;0.092305465450567336649356775524211;0.0936847442823852127880002171878;0.095073187478842358100195042425185;0.09647076372386198528374734451063;0.097877441495373140867286565480754;0.099293189066021692035235446383012;0.10071797450388575434487847815035;0.1021517656731961709581923969381;0.10359453023506115521001902379794;0.10504623564819570713524399252492;0.10650684916965552639922520938853;0.1079763378555757546983784322947;0.10945466856191377047480273176916;0.11094180794519681310106307137175;0.11243772246327410346822261999478;0.11394237837607329444367110227176;0.11545574174636152875450534338597;0.11697777844051099327415954576281;0.11850845412926847011192421632586;0.12004773428852993921722713821509;0.12159558420011912227565176181088;0.1231519689525706895416590214154;0.12471685344191746347419780249766;0.12629020237248228530901883459592;0.12787198025767421150078462233068;0.12946215142078859594576556446555;0.13106067999581216820814688617247;0.13266752992823177548231683431368;0.13428266497584756544725337334967;0.13590604870959038796840445684211;0.13753764451434363769166679958289;0.13917741558976892690679960651323;0.14082532495113619930293680226896;0.14248133543015784052698791128932;0.14414540967582700758953251352068;0.14581751015526028814051073823066;0.14749759915454385694744132706546;0.14918563877958429531034312276461;0.15088159095696357381299890221271;0.15258541743479731023214185370307;0.15429707978359774589449671111652;0.15601653939714066332555830740603;0.1577437574933358011008976973244;0.15947869511510193163417170580942;0.16122131313124526963420635183866;0.16297157223734226594302754165255;0.1647294329566259540875705624785;0.1664948556408764601677319205919;0.16826780047131500994694874862034;0.17004822745950243234602794473176;0.17183609644824088258374672477657;0.17363136711247950660919059373555;0.17543399896022404682582873647334;0.1772439513334501670627219027665;0.17906118340902038577056032409018;0.18088565419960500602059028096846;0.18271732255460632066146331453638;0.1845561471610870918347302449547;0.18640208654470197258135044648952;0.18825509907063320280684592944453;0.19011514294452974693783176007855;0.19198217621344965122531789347704;0.19385615676680656438435335076065;0.19573704233731942236929057798989;0.19762479050196574137387983682856;0.19951935868293868558964732073946;0.20142070414860685501068360281351;0.20332878401447890270858920302999;0.20524355524417015050886448079837;0.20716497465037320147018817806384;0.2090929988958327712111895380076;0.21102758449432224008290859273984;0.21296868781162520134486726419709;0.2149162650665191742760384840949;0.21687027233176314755525027067051;0.21883066553508856433296614341089;0.22079740046019319388292956318764;0.22277043274773850045633594163519;0.22474971789635006524932236970926;0.2267352112636212280172287591995;0.22872686806712028140253778474289;0.23072464338540044082037638872862;0.23272849215901270092388131160988;0.23473836919152257785015081026359;0.23675422915052951600145547672582;0.23877602656868873731710323227162;0.24080371584473742041510035960528;0.24283725124452310017986178536376;0.24487658690203506495208785054274;0.24692167682043858478735387507186;0.24897247487311280345068098540651;0.25102893480469112841291234872187;0.25309101023210411884889481370919;0.25515865464562625941624673941988;0.25723182140992395527945291178185;0.25931046376510846762641904206248;0.26139453482779029247495827803505;0.26348398759213587094762942797388;0.26557877493092874043867368527572;0.26767884959663224009318582830019;0.26978416422245476979924205807038;0.27189467132341854638255540521641;0.27401032329743024718027299968526;0.27613107242635515081730090969359;0.27825687087709327638407330596237;0.28038767070265774306037087626464;0.28252342384325679347512050298974;0.28466408212737770444533680347377;0.28680959727287308469456661441654;0.28895992088804967057313888290082;0.29111500447276039693633720162325;0.29327479941949807784595805060235;0.29543925701449103016216213291045;0.29760832843880313802742421103176;0.29978196476943363979472678693128;0.30196011698042157789245720778126;0.30414273594395102584542200929718;0.30632977243145909085342282196507;0.30852117711474680294969630267587;0.3107169005670910033600762290007;0.31291689326436000762043931899825;0.31512110558612949073875597605365;0.3173294878168024801823321467964;0.31954199014673079215498319172184;0.32175856267333791116413976851618;0.32397915540224497821242266581976;0.32620371824839777818993979963125;0.32843220103719739100256447272841;0.33066455350563117576712102163583;0.33290072530340619749722463893704;0.33514066599408576241359014602494;0.33738432505622628632124815339921;0.33963165188451716058892770888633;0.34188259579092178386261480227404;0.34413710600582092524746258277446;0.34639513167915836344690205805819;0.34865662188158708101326510586659;0.35092152560561823415596904851554;0.35318979176677173237308693387604;0.35546136920472837239515229157405;0.35773620668448380399695452069864;0.36001425289750355052120767140877;0.36229545646288152660474679578329;0.3645797659284973901705484422564;0.36686712977217839082300088193733;0.36915749640286060762051079109369;0.37145081416175262933876410897938;0.37374703132350128864658245220198;0.37604609609735772934868691663723;0.37834795662834563856335989839863;0.38065256099843108872349262128409;0.38295985722769332326720359560568;0.3852697932754972631741452460119;0.38758231704166712372483516446664;0.38989737636766153006107060718932;0.39221491903775018705857746681431;0.39453489278019154840038140719116;0.39685724526841131831744746705226;0.39918192412218334030882260776707;0.40150887690881059688408072361199;0.40383805114430815219606074606418;0.40616939429458620569590721061104;0.4085028537766360323679748489667;0.41083837695971509029746471242106;0.41317591116653479277331939556461;0.41551540367444789181305964120838;0.41785680171663808213367019561701;0.42020005248331032676745167009358;0.42254510312288173778938471514266;0.42489190074317328971176266350085;0.42724039241260347576911726719118;0.42959052516138163113623704703059;0.43194224598270308801417627364572;0.43429550183394410867165902345732;0.43665023963785898342138125372003;0.43900640628377674001825425875722;0.44136394862879907430297521386819;0.44372281349899916902401741936046;0.44608294769062067919307423835562;0.44844429797127816073043504729867;0.450806811081157610132663648983;0.45317043373421717067373037934885;0.45553511261938994802989100207924;0.45790079440178566017038974678144;0.46026742572389406360500174741901;0.46263495320678793554236563068116;0.46500332345132738831594565453997;0.46737248303936435034344754058111;0.46974237853494738015314169388148;0.47211295648552631387673272911343;0.47448416342315868909906839689938;0.47685594586571533604058004129911;0.47922825031808674589584029490652;0.48160102327338916161636461765738;0.4839742112141723340279497733718;0.48634776061362583465808029359323;0.4887216179367867008309644916153;0.49109572964174674769566308896174;0.49347004218085999127652030438185;0.49584450200195145930237572429178;0.49821905554952328198936584158218;0.50059364926596450207085808870033;0.50296822959275733211370607023127;0.50534274297168646494782251465949;0.50771713584604682978351775091141;0.5100913546618505156615697160305;0.51246534586903647046085552574368;0.51483905592267620310309439446428;0.51721243128418381562738659340539;0.51958541842252115028344405800453;0.52195796381540726649461703345878;0.52433001395052414306263699472765;0.52670151532672448979610635433346;0.52907241445523800482675369494245;0.53144265786087785397029392697732;0.53381219208324748315419583377661;0.53618096367794521039940036644111;0.53854891921777059415887833893066;0.54091600529392891427704626039485;0.54328216851723665214990433014464;0.54564735551932408430531040721689;0.5480115129538408735854204678617;0.550374587497657663526240412466;0.55273652585207033727243697285303;0.55509727474400061275616735656513;0.55745678092719830321044582888135;0.55981499118344291154869551974116;0.56217185232374244918673866777681;0.56452731118953503042234842723701;0.56688131465388580387809724925319;0.569233809622686992568674213544;0.57158474303585404818761617207201;0.5739340618685235817508782929508;0.57628171313224829663823811642942;0.57862764387619258776851438597078;0.58097180118832758566327356675174;0.58331413219662286984146248869365;0.58565458407024062470469516483718;0.58799310402072613168655834670062;0.59032963930319948264724416731042;0.59266413721754362953220152121503;0.5949965451095949875437440823589;0.59732681037232904230904750875197;0.59965488044704895465031313506188;0.60198070282456905832901838948601;0.60430422504640035619161153590539;0.60662539470593368484685470320983;0.60894415944962088094172258934123;0.61126046697815716868262825300917;0.61357426504765877339764301723335;0.61588550147084308861167301074602;0.61819412411820429120723474625265;0.62050008091919051089746517391177;0.62280331986337666982933569670422;0.62510378900163954263291543611558;0.62740143644732726535551137203583;0.62969621037743139790876512051909;0.63198805903375498971286106097978;0.63427693072407964614001230074791;0.63656277382333270598024910214008;0.63884553677475008903741127141984;0.6411251680910403649704676354304;0.6434016163555449363542493301793;0.64567483022339933196320771457977;0.64794475842268917098465408344055;0.65021134975560856972265355580021;0.65247455309961366332061061257264;0.65473431740857579441694724664558;0.65699059171393381362236141285393;0.65924332512584216114959190235822;0.66149246683432016968851030469523;0.66373796611039670434450954417116;0.66597977230725580177761457889574;0.66821783486137720231567982409615;0.67045210329367899149133336322848;0.67268252721065380228537833318114;0.67490905630550734883854602230713;0.67713164035929218620424308028305;0.67935022924204013783366917778039;0.68156477291389405692711989104282;0.68377522142623514689319108583732;0.68598152492281050385258822643664;0.68818363364085710642825688410085;0.69038149791222469531248862040229;0.69257506816449532216495299508097;0.69476429492210201033230987377465;0.69694912880744452898795771034202;0.69912952054200272478112765384139;0.70130542094744907632986041789991;0.70347678094675636373267479939386;0.70564355156530578216944604719174;0.707805683931990947677093117818;0.709963129280320903724543768476;0.71211583894951857587329868692905;0.71426376438562022563871778402245;0.71640685714256879812467104784446;0.71854506888330815783660909801256;0.72067835138087199542411553920829;0.72280665651947229033424946464947;0.72492993629558466484041900912416;0.72704814281903029637987856403925;0.72916122831405749682431860492215;0.73126914512041751859072746810853;0.7333718456944412489306728275551;0.73546928261010990901525019580731;0.73756140856012630813154373754514;0.73964817635698043574166149483062;0.74172953893401494251946814983967;0.74380544934648584742831189942081;0.74587586077262169048651685443474;0.74794072651468002099761633871822;0.74999999999999988897769753748435;0.75205363478205300431511659553507;0.75410158454149045503811521484749;0.75614380308718842638171508951928;0.75818024435728936794021137757227;0.76021086242024105139591938495869;0.76223561147583263064575476164464;0.76425444585622770432564720977098;0.76626732002699426971048524137586;0.76827418858813145696728952316334;0.77027500627509426500694189599017;0.77226972795981363439921096869512;0.7742583086517149659755432367092;0.77624070349873219853975570003968;0.77821686778832055431109893106623;0.78018675694846340018528962900746;0.78215032654867955308475302445004;0.784107532301023146814600295329;0.78605833006108472016393307058024;0.78800267582898531060209279530682;0.78994052575036977081879285833566;0.7918718361173949782383374440542;0.79379656336971682328851329657482;0.79571466409547197962126574566355;0.79762609503225700979811563229305;0.79953081306810469541801467130426;0.80142877524245559328619492589496;0.80331993874712770420387641934212;0.80520426092728158984357378358254;0.80708169928238282508914380741771;0.80895221146716034255064187163953;0.81081575529256111334319712113938;0.81267228872670305150904823676683;0.81452176989582114607912899373332;0.81636415708521359313465382001596;0.81819940874018171061976545388461;0.82002748346696752168583088860032;0.82184834003368700816594127900316;0.8236619373712610325810601352714;0.82546823457434048698644346586661;0.82726719090222966546122052022838;0.82905876577980497366127110581147;0.83084291879842964156921425455948;0.83261960971686610477604517654981;0.83438879846218294566995155037148;0.83615044513065850395605593803339;0.83790450998868126752938678691862;0.83965095347364671063417063123779;0.84138973619484813681879131763708;0.84312081893436674473463199319667;0.84484416264795458850755949242739;0.84655972846591631686408163659507;0.84826747769398591625389371984056;0.84996737181419823592420925706392;0.85165937248575984686027595671476;0.85334344154591135200860207987716;0.85501954101079014058939264941728;0.85668763307628603698162805812899;0.85834768011889439609518603901961;0.85999964469656453580626020993805;0.86164348954954395054528504260816;0.86327917760121963830499680625508;0.86490667195895287733264922280796;0.86652593591491311464380942197749;0.86813693294690430501958644526894;0.86973962671918958466932281226036;0.87133398108331050480046542361379;0.87291996007890237940785027603852;0.8744975279345055252377960641752;0.87606664906837194983779681933811;0.87762728808926726564720866008429;0.87917940979727082773109714253224;0.88072297918456721177449253445957;0.88225796143623735900973770185374;0.88378432193104394798410794464871;0.88530202624221099316770278164768;0.88681104013820155618219587267959;0.88831132958348923978064703987911;0.88980286073932601809133302595001;0.89128559996450573699178221431794;0.8927595138161221743899886860163;0.89422456905032376983655240110238;0.89568073262306391324472087944741;0.89712797169084534942840036819689;0.89856625361146125197109313376131;0.89999554594473196722503871569643;0.90141581645323576310602220473811;0.90282703310303724641983080800856;0.90422916406440834169444542567362;0.90562217771254749365539282734971;0.90700604262829243040755500260275;0.90838072759882837470257754830527;0.90974620161839281351490171800833;0.91110243388897460548037088301498;0.91244939382100842539813356779632;0.9137870510340646568181455222657;0.91511537535753506578117821845808;0.91643433683131259037679683387978;0.91774390570646813269917174693546;0.91904405244592024537553243135335;0.92033474772510248662626963778166;0.92161596243262366989767997438321;0.92288766767092600407096369963256;0.9241498347569354621100501390174;0.92540243522270904108495415130164;0.92664544081607780334763901919359;0.92787882350128270125821927649667;0.92910255545960795942050935991574;0.9303166090900081286463318974711;0.93152095700973025493851764622377;0.93271557205493216269331924195285;0.93390042728129496474309689801885;0.93507549596463035435078836599132;0.93624075160148412244609517074423;0.93739616790973290250121863209642;0.93854171882917802882673186104512;0.93967737852213262250700154254446;0.94080312137400445848811614268925;0.94191892199387416972911069024121;0.94302475521506712308195119476295;0.9441205960957219645024451892823;0.94520641991935228087839959698613;0.94628220219540482016640225992887;0.94734791865981149427966556686442;0.9484035452755366080168641929049;0.94944905823311898096505956345936;0.95048443395120951748822335503064;0.95150964907710244844452063261997;0.9525246804872621320114944865054;0.95352950528784496952994231833145;0.95452410081521532614345915135345;0.95550844463645723259048736508703;0.95648251454987942565821867901832;0.95744628858551728001202718587592;0.95839974500562763459754478390096;0.95934286230517917815063810849097;0.96027561921233739461456480057677;0.96119799468894473459812388682622;0.96210996793099468060717072148691;0.96301151836910126036173096508719;0.96390262566896278695338651232305;0.96478326973182060299905060674064;0.96565343069491293981343460472999;0.96651308893192133808724975096993;0.96736222505341551425317447865382;0.96820081990728856791150747085339;0.96902885457919052392128378414782;0.96984631039295421395252105867257;0.9706531689110162730571573774796;0.97144941193483402841479801281821;0.97223502150529461651728979632026;0.9730099799031211027511290012626;0.97377426964927171759711654885905;0.97452787350533431887100732637919;0.97527077447391452569291914187488;0.97600295579901996667615549085895;0.97672440096643753371097318449756;0.97743509370410674996776378975483;0.97813501798248536633906269344152;0.97882415801491229334629906588816;0.9795024982579629835299783735536;0.98017002341179981783625407842919;0.98082671842051816213370329933241;0.98147256847248443012432517207344;0.98210755900067159274158257176168;0.98273167568298702700957392153214;0.98334490444259559094319911309867;0.98394723144823714733320230152458;0.9845386431145388694829989617574;0.98511912610232110765196011925582;0.9856886673188984815396906924434;0.98624725391837553267748717189534;0.9867948733019357154816475485859;0.98733151311812628048159012905671;0.98785716126313638518752213713014;0.98837180588107065304370735248085;0.98887543536421551593207368568983;0.98936803835330255907365426537581;0.98984960373776331721273891162127;0.99032012065598040706504434638191;0.99077957849553266456155142805073;0.99122796689343461995491679772385;0.99166527573636975567694662458962;0.99209149516091865717015707559767;0.99250661555378205669342150940793;0.99291062755199710476716745688464;0.99330352204314864561496278838604;0.99368529016557483046767629275564;0.99405592330856717975251513053081;0.99441541311256420598851946124341;0.99476375146934081783456349512562;0.99510093052219028564309155626688;0.99542694266610221021096549520735;0.99574178054793371916986188807641;0.99604543706657500123924364743289;0.99633790537311028856493066996336;0.9966191788709715115857079581474;0.99688925121608740198553277878091;0.99714811631702682248601377068553;0.99739576833513576836764968902571;0.9976322016846692619651548739057;0.99785741103291725195845174312126;0.99807139130032496154854015912861;0.99827413766060768551824367023073;0.99846564554085903697711046334007;0.99864591062165453116961089108372;0.99881492883714906305669956054771;0.99897269637516816764843952114461;0.99911920967729472842222548933933;0.99925446543894858031364947237307;0.99937846060946111670375557878288;0.999491192392144789380381553201;0.99959265824435505898293286008993;0.99968285587754857068887304194504;0.99976178325733466856206632655812;0.99982943860352102571908972095116;0.99988582039015394542502690455876;0.99993092734555277800723160908092;0.99996475845233878665396787255304;0.99998731294745724085260007996112;0.99999859032219606813640666587162;0.99999859032219606813640666587162;0.99998731294745724085260007996112;0.99996475845233878665396787255304;0.99993092734555277800723160908092;0.99988582039015394542502690455876;0.99982943860352102571908972095116;0.99976178325733466856206632655812;0.99968285587754857068887304194504;0.99959265824435505898293286008993;0.999491192392144789380381553201;0.99937846060946111670375557878288;0.99925446543894858031364947237307;0.99911920967729472842222548933933;0.99897269637516816764843952114461;0.99881492883714906305669956054771;0.99864591062165453116961089108372;0.99846564554085903697711046334007;0.99827413766060768551824367023073;0.99807139130032496154854015912861;0.99785741103291725195845174312126;0.9976322016846692619651548739057;0.99739576833513576836764968902571;0.99714811631702682248601377068553;0.99688925121608740198553277878091;0.9966191788709715115857079581474;0.99633790537311028856493066996336;0.99604543706657500123924364743289;0.99574178054793371916986188807641;0.99542694266610221021096549520735;0.99510093052219028564309155626688;0.99476375146934081783456349512562;0.99441541311256420598851946124341;0.99405592330856717975251513053081;0.99368529016557483046767629275564;0.99330352204314864561496278838604;0.99291062755199710476716745688464;0.99250661555378205669342150940793;0.99209149516091865717015707559767;0.99166527573636975567694662458962;0.99122796689343461995491679772385;0.99077957849553266456155142805073;0.99032012065598040706504434638191;0.98984960373776331721273891162127;0.98936803835330255907365426537581;0.98887543536421551593207368568983;0.98837180588107065304370735248085;0.98785716126313638518752213713014;0.98733151311812628048159012905671;0.9867948733019357154816475485859;0.98624725391837553267748717189534;0.9856886673188984815396906924434;0.98511912610232110765196011925582;0.9845386431145388694829989617574;0.98394723144823714733320230152458;0.98334490444259559094319911309867;0.98273167568298702700957392153214;0.98210755900067159274158257176168;0.98147256847248443012432517207344;0.98082671842051816213370329933241;0.98017002341179981783625407842919;0.9795024982579629835299783735536;0.97882415801491229334629906588816;0.97813501798248536633906269344152;0.97743509370410674996776378975483;0.97672440096643753371097318449756;0.97600295579901996667615549085895;0.97527077447391452569291914187488;0.97452787350533431887100732637919;0.97377426964927171759711654885905;0.9730099799031211027511290012626;0.97223502150529461651728979632026;0.97144941193483402841479801281821;0.9706531689110162730571573774796;0.96984631039295421395252105867257;0.96902885457919052392128378414782;0.96820081990728856791150747085339;0.96736222505341551425317447865382;0.96651308893192133808724975096993;0.96565343069491293981343460472999;0.96478326973182060299905060674064;0.96390262566896278695338651232305;0.96301151836910126036173096508719;0.96210996793099468060717072148691;0.96119799468894473459812388682622;0.96027561921233739461456480057677;0.95934286230517917815063810849097;0.95839974500562763459754478390096;0.95744628858551728001202718587592;0.95648251454987942565821867901832;0.95550844463645723259048736508703;0.95452410081521532614345915135345;0.95352950528784496952994231833145;0.9525246804872621320114944865054;0.95150964907710244844452063261997;0.95048443395120951748822335503064;0.94944905823311898096505956345936;0.9484035452755366080168641929049;0.94734791865981149427966556686442;0.94628220219540482016640225992887;0.94520641991935228087839959698613;0.9441205960957219645024451892823;0.94302475521506712308195119476295;0.94191892199387416972911069024121;0.94080312137400445848811614268925;0.93967737852213262250700154254446;0.93854171882917802882673186104512;0.93739616790973290250121863209642;0.93624075160148412244609517074423;0.93507549596463035435078836599132;0.93390042728129496474309689801885;0.93271557205493216269331924195285;0.93152095700973025493851764622377;0.9303166090900081286463318974711;0.92910255545960795942050935991574;0.92787882350128270125821927649667;0.92664544081607780334763901919359;0.92540243522270904108495415130164;0.9241498347569354621100501390174;0.92288766767092600407096369963256;0.92161596243262366989767997438321;0.92033474772510248662626963778166;0.91904405244592024537553243135335;0.91774390570646813269917174693546;0.91643433683131259037679683387978;0.91511537535753506578117821845808;0.9137870510340646568181455222657;0.91244939382100842539813356779632;0.91110243388897460548037088301498;0.90974620161839281351490171800833;0.90838072759882837470257754830527;0.90700604262829243040755500260275;0.90562217771254749365539282734971;0.90422916406440834169444542567362;0.90282703310303724641983080800856;0.90141581645323576310602220473811;0.89999554594473196722503871569643;0.89856625361146125197109313376131;0.89712797169084534942840036819689;0.89568073262306391324472087944741;0.89422456905032376983655240110238;0.8927595138161221743899886860163;0.89128559996450573699178221431794;0.88980286073932601809133302595001;0.88831132958348923978064703987911;0.88681104013820155618219587267959;0.88530202624221099316770278164768;0.88378432193104394798410794464871;0.88225796143623735900973770185374;0.88072297918456721177449253445957;0.87917940979727082773109714253224;0.87762728808926726564720866008429;0.87606664906837194983779681933811;0.8744975279345055252377960641752;0.87291996007890237940785027603852;0.87133398108331050480046542361379;0.86973962671918958466932281226036;0.86813693294690430501958644526894;0.86652593591491311464380942197749;0.86490667195895287733264922280796;0.86327917760121963830499680625508;0.86164348954954395054528504260816;0.85999964469656453580626020993805;0.85834768011889439609518603901961;0.85668763307628603698162805812899;0.85501954101079014058939264941728;0.85334344154591135200860207987716;0.85165937248575984686027595671476;0.84996737181419823592420925706392;0.84826747769398591625389371984056;0.84655972846591631686408163659507;0.84484416264795458850755949242739;0.84312081893436674473463199319667;0.84138973619484813681879131763708;0.83965095347364671063417063123779;0.83790450998868126752938678691862;0.83615044513065850395605593803339;0.83438879846218294566995155037148;0.83261960971686610477604517654981;0.83084291879842964156921425455948;0.82905876577980497366127110581147;0.82726719090222966546122052022838;0.82546823457434048698644346586661;0.8236619373712610325810601352714;0.82184834003368700816594127900316;0.82002748346696752168583088860032;0.81819940874018171061976545388461;0.81636415708521359313465382001596;0.81452176989582114607912899373332;0.81267228872670305150904823676683;0.81081575529256111334319712113938;0.80895221146716034255064187163953;0.80708169928238282508914380741771;0.80520426092728158984357378358254;0.80331993874712770420387641934212;0.80142877524245559328619492589496;0.79953081306810469541801467130426;0.79762609503225700979811563229305;0.79571466409547197962126574566355;0.79379656336971682328851329657482;0.7918718361173949782383374440542;0.78994052575036977081879285833566;0.78800267582898531060209279530682;0.78605833006108472016393307058024;0.784107532301023146814600295329;0.78215032654867955308475302445004;0.78018675694846340018528962900746;0.77821686778832055431109893106623;0.77624070349873219853975570003968;0.7742583086517149659755432367092;0.77226972795981363439921096869512;0.77027500627509426500694189599017;0.76827418858813145696728952316334;0.76626732002699426971048524137586;0.76425444585622770432564720977098;0.76223561147583263064575476164464;0.76021086242024105139591938495869;0.75818024435728936794021137757227;0.75614380308718842638171508951928;0.75410158454149045503811521484749;0.75205363478205300431511659553507;0.74999999999999988897769753748435;0.74794072651468002099761633871822;0.74587586077262169048651685443474;0.74380544934648584742831189942081;0.74172953893401494251946814983967;0.73964817635698043574166149483062;0.73756140856012630813154373754514;0.73546928261010990901525019580731;0.7333718456944412489306728275551;0.73126914512041751859072746810853;0.72916122831405749682431860492215;0.72704814281903029637987856403925;0.72492993629558466484041900912416;0.72280665651947229033424946464947;0.72067835138087199542411553920829;0.71854506888330815783660909801256;0.71640685714256879812467104784446;0.71426376438562022563871778402245;0.71211583894951857587329868692905;0.709963129280320903724543768476;0.707805683931990947677093117818;0.70564355156530578216944604719174;0.70347678094675636373267479939386;0.70130542094744907632986041789991;0.69912952054200272478112765384139;0.69694912880744452898795771034202;0.69476429492210201033230987377465;0.69257506816449532216495299508097;0.69038149791222469531248862040229;0.68818363364085710642825688410085;0.68598152492281050385258822643664;0.68377522142623514689319108583732;0.68156477291389405692711989104282;0.67935022924204013783366917778039;0.67713164035929218620424308028305;0.67490905630550734883854602230713;0.67268252721065380228537833318114;0.67045210329367899149133336322848;0.66821783486137720231567982409615;0.66597977230725580177761457889574;0.66373796611039670434450954417116;0.66149246683432016968851030469523;0.65924332512584216114959190235822;0.65699059171393381362236141285393;0.65473431740857579441694724664558;0.65247455309961366332061061257264;0.65021134975560856972265355580021;0.64794475842268917098465408344055;0.64567483022339933196320771457977;0.6434016163555449363542493301793;0.6411251680910403649704676354304;0.63884553677475008903741127141984;0.63656277382333270598024910214008;0.63427693072407964614001230074791;0.63198805903375498971286106097978;0.62969621037743139790876512051909;0.62740143644732726535551137203583;0.62510378900163954263291543611558;0.62280331986337666982933569670422;0.62050008091919051089746517391177;0.61819412411820429120723474625265;0.61588550147084308861167301074602;0.61357426504765877339764301723335;0.61126046697815716868262825300917;0.60894415944962088094172258934123;0.60662539470593368484685470320983;0.60430422504640035619161153590539;0.60198070282456905832901838948601;0.59965488044704895465031313506188;0.59732681037232904230904750875197;0.5949965451095949875437440823589;0.59266413721754362953220152121503;0.59032963930319948264724416731042;0.58799310402072613168655834670062;0.58565458407024062470469516483718;0.58331413219662286984146248869365;0.58097180118832758566327356675174;0.57862764387619258776851438597078;0.57628171313224829663823811642942;0.5739340618685235817508782929508;0.57158474303585404818761617207201;0.569233809622686992568674213544;0.56688131465388580387809724925319;0.56452731118953503042234842723701;0.56217185232374244918673866777681;0.55981499118344291154869551974116;0.55745678092719830321044582888135;0.55509727474400061275616735656513;0.55273652585207033727243697285303;0.550374587497657663526240412466;0.5480115129538408735854204678617;0.54564735551932408430531040721689;0.54328216851723665214990433014464;0.54091600529392891427704626039485;0.53854891921777059415887833893066;0.53618096367794521039940036644111;0.53381219208324748315419583377661;0.53144265786087785397029392697732;0.52907241445523800482675369494245;0.52670151532672448979610635433346;0.52433001395052414306263699472765;0.52195796381540726649461703345878;0.51958541842252115028344405800453;0.51721243128418381562738659340539;0.51483905592267620310309439446428;0.51246534586903647046085552574368;0.5100913546618505156615697160305;0.50771713584604682978351775091141;0.50534274297168646494782251465949;0.50296822959275733211370607023127;0.50059364926596450207085808870033;0.49821905554952328198936584158218;0.49584450200195145930237572429178;0.49347004218085999127652030438185;0.49109572964174674769566308896174;0.4887216179367867008309644916153;0.48634776061362583465808029359323;0.4839742112141723340279497733718;0.48160102327338916161636461765738;0.47922825031808674589584029490652;0.47685594586571533604058004129911;0.47448416342315868909906839689938;0.47211295648552631387673272911343;0.46974237853494738015314169388148;0.46737248303936435034344754058111;0.46500332345132738831594565453997;0.46263495320678793554236563068116;0.46026742572389406360500174741901;0.45790079440178566017038974678144;0.45553511261938994802989100207924;0.45317043373421717067373037934885;0.450806811081157610132663648983;0.44844429797127816073043504729867;0.44608294769062067919307423835562;0.44372281349899916902401741936046;0.44136394862879907430297521386819;0.43900640628377674001825425875722;0.43665023963785898342138125372003;0.43429550183394410867165902345732;0.43194224598270308801417627364572;0.42959052516138163113623704703059;0.42724039241260347576911726719118;0.42489190074317328971176266350085;0.42254510312288173778938471514266;0.42020005248331032676745167009358;0.41785680171663808213367019561701;0.41551540367444789181305964120838;0.41317591116653479277331939556461;0.41083837695971509029746471242106;0.4085028537766360323679748489667;0.40616939429458620569590721061104;0.40383805114430815219606074606418;0.40150887690881059688408072361199;0.39918192412218334030882260776707;0.39685724526841131831744746705226;0.39453489278019154840038140719116;0.39221491903775018705857746681431;0.38989737636766153006107060718932;0.38758231704166712372483516446664;0.3852697932754972631741452460119;0.38295985722769332326720359560568;0.38065256099843108872349262128409;0.37834795662834563856335989839863;0.37604609609735772934868691663723;0.37374703132350128864658245220198;0.37145081416175262933876410897938;0.36915749640286060762051079109369;0.36686712977217839082300088193733;0.3645797659284973901705484422564;0.36229545646288152660474679578329;0.36001425289750355052120767140877;0.35773620668448380399695452069864;0.35546136920472837239515229157405;0.35318979176677173237308693387604;0.35092152560561823415596904851554;0.34865662188158708101326510586659;0.34639513167915836344690205805819;0.34413710600582092524746258277446;0.34188259579092178386261480227404;0.33963165188451716058892770888633;0.33738432505622628632124815339921;0.33514066599408576241359014602494;0.33290072530340619749722463893704;0.33066455350563117576712102163583;0.32843220103719739100256447272841;0.32620371824839777818993979963125;0.32397915540224497821242266581976;0.32175856267333791116413976851618;0.31954199014673079215498319172184;0.3173294878168024801823321467964;0.31512110558612949073875597605365;0.31291689326436000762043931899825;0.3107169005670910033600762290007;0.30852117711474680294969630267587;0.30632977243145909085342282196507;0.30414273594395102584542200929718;0.30196011698042157789245720778126;0.29978196476943363979472678693128;0.29760832843880313802742421103176;0.29543925701449103016216213291045;0.29327479941949807784595805060235;0.29111500447276039693633720162325;0.28895992088804967057313888290082;0.28680959727287308469456661441654;0.28466408212737770444533680347377;0.28252342384325679347512050298974;0.28038767070265774306037087626464;0.27825687087709327638407330596237;0.27613107242635515081730090969359;0.27401032329743024718027299968526;0.27189467132341854638255540521641;0.26978416422245476979924205807038;0.26767884959663224009318582830019;0.26557877493092874043867368527572;0.26348398759213587094762942797388;0.26139453482779029247495827803505;0.25931046376510846762641904206248;0.25723182140992395527945291178185;0.25515865464562625941624673941988;0.25309101023210411884889481370919;0.25102893480469112841291234872187;0.24897247487311280345068098540651;0.24692167682043858478735387507186;0.24487658690203506495208785054274;0.24283725124452310017986178536376;0.24080371584473742041510035960528;0.23877602656868873731710323227162;0.23675422915052951600145547672582;0.23473836919152257785015081026359;0.23272849215901270092388131160988;0.23072464338540044082037638872862;0.22872686806712028140253778474289;0.2267352112636212280172287591995;0.22474971789635006524932236970926;0.22277043274773850045633594163519;0.22079740046019319388292956318764;0.21883066553508856433296614341089;0.21687027233176314755525027067051;0.2149162650665191742760384840949;0.21296868781162520134486726419709;0.21102758449432224008290859273984;0.2090929988958327712111895380076;0.20716497465037320147018817806384;0.20524355524417015050886448079837;0.20332878401447890270858920302999;0.20142070414860685501068360281351;0.19951935868293868558964732073946;0.19762479050196574137387983682856;0.19573704233731942236929057798989;0.19385615676680656438435335076065;0.19198217621344965122531789347704;0.19011514294452974693783176007855;0.18825509907063320280684592944453;0.18640208654470197258135044648952;0.1845561471610870918347302449547;0.18271732255460632066146331453638;0.18088565419960500602059028096846;0.17906118340902038577056032409018;0.1772439513334501670627219027665;0.17543399896022404682582873647334;0.17363136711247950660919059373555;0.17183609644824088258374672477657;0.17004822745950243234602794473176;0.16826780047131500994694874862034;0.1664948556408764601677319205919;0.1647294329566259540875705624785;0.16297157223734226594302754165255;0.16122131313124526963420635183866;0.15947869511510193163417170580942;0.1577437574933358011008976973244;0.15601653939714066332555830740603;0.15429707978359774589449671111652;0.15258541743479731023214185370307;0.15088159095696357381299890221271;0.14918563877958429531034312276461;0.14749759915454385694744132706546;0.14581751015526028814051073823066;0.14414540967582700758953251352068;0.14248133543015784052698791128932;0.14082532495113619930293680226896;0.13917741558976892690679960651323;0.13753764451434363769166679958289;0.13590604870959038796840445684211;0.13428266497584756544725337334967;0.13266752992823177548231683431368;0.13106067999581216820814688617247;0.12946215142078859594576556446555;0.12787198025767421150078462233068;0.12629020237248228530901883459592;0.12471685344191746347419780249766;0.1231519689525706895416590214154;0.12159558420011912227565176181088;0.12004773428852993921722713821509;0.11850845412926847011192421632586;0.11697777844051099327415954576281;0.11545574174636152875450534338597;0.11394237837607329444367110227176;0.11243772246327410346822261999478;0.11094180794519681310106307137175;0.10945466856191377047480273176916;0.1079763378555757546983784322947;0.10650684916965552639922520938853;0.10504623564819570713524399252492;0.10359453023506115521001902379794;0.1021517656731961709581923969381;0.10071797450388575434487847815035;0.099293189066021692035235446383012;0.097877441495373140867286565480754;0.09647076372386198528374734451063;0.095073187478842358100195042425185;0.0936847442823852127880002171878;0.092305465450567336649356775524211;0.090935382092764971417864217073657;0.089574525110952041284662072939682;0.088222925199003432439326388703194;0.086880612842002546969411014288198;0.085547618315553630718994782000664;0.084223971685099041639688266513986;0.082909702805241181078343970511924;0.081604841319068810445713779699872;0.080309416657488919000229543598834;0.079023458038562588434672306902939;0.077746994466846075511057279072702;0.076480054732736613143373460843577;0.075222667411823096461631621423294;0.073974860864241431812615701346658;0.072736663234035159320001184823923;0.071508102448520238780815816426184;0.070289206217655719743930831100442;0.06908000203341801981338221594342;0.067880517169181586734083566625486;0.066690778679103335235822669346817;0.065510813397512468458927514802781;0.064340647938305295383543125353754;0.063180308694345155284821657915018;0.062029821836866561035606082441518;0.060889213314885726191505455062725;0.059758508854614589278497760460596;0.058637733958880777773714498835034;0.057526913906552734623289779847255;0.056426073751968952585400529642357;0.055335238324373370311093367490685;0.054254432227355209317209983055363;0.053183679838293862474074558122084;0.052123005307809389119455545369419;0.051072432559217451064625947765308;0.050031985287990077271302880035364;0.049001686961220980442988093273016;0.04798156081709631370912916281668;0.046971629864370534335193951847032;0.045971916881847485480960813220008;0.044982444417866696007024529535556;0.044003234789794509751459372637328;0.043034310083521154499663907699869;0.042075692152962140824001835426316;0.041127402619565822661229503864888;0.040189462871825232248568227078067;0.039261894064796187819865735946223;0.038344717119619620149251204566099;0.037437952723050060832576946268091;0.036541621326989126572470922837965;0.035655743148023777422395141911693;0.034780338166970736768490723989089;0.0339154261284257407815800888784;0.033061026540318172450838574150112;0.032217158673470969176833023084328;0.031383841561166136990834729658673;0.030561093998715427311196890514111;0.029748934543036231747947795156506;0.028947381512233305578263298230013;0.028156452985185376203247642479255;0.027376166801137580275593563783332;0.026606540559298896830853209394263;0.025847591618445353578437106989441;0.02509933709652845124082887195982;0.024361793870289027985620577965165;0.02363497857487673048382248452981;0.022918907603474591994086040358525;0.022213597106929605651259862497682;0.021519062993388182736254066185211;0.020835320927937328594481414256734;0.02016238633225159171402651736571;0.019500274384245008807425847408012;0.018849000017728712030873339244863;0.018208577922074309363154043239774;0.017579022541882538543944747289061;0.016960348076657194571481568345916;0.016352568480485274449165444821119;0.015755697461721951402324748414685;0.015169748482681433277008409277187;0.01459473475933348307620462946943;0.014030669261005046521972872142214;0.01347756471008809686651375159272;0.012935433581752309173396042751847;0.012404288103663951847721591548179;0.01188414025570999621450596350769;0.011375001769727999256787143167458;0.010876884129241204401949971725116;0.010389798569200026090442179338424;0.009913756075728086258891380566638;0.0094487673858749121613698207511334;0.0089948429873734636608162418269785;0.0085519931184036557247907239798224;0.008120227767361598569806346858968;0.0076995566726339448315741265105316;0.0072899893223787315399420094763627;0.0068915349543108850305372925504344;0.0065042025554942206611030997009948;0.0061280008621386050648993659706321;0.0057629383594029470749831034481758;0.0054090232812036287413093305076472;0.0050662636100292091079211331816623;0.0047346670767599019491456147079589;0.0044142411604936038216351334995124;0.0041049930883769181200193543190835;0.0038069298354423408703439690725645;0.0035200581244507755940276183537208;0.0032443844257400433761517888342496;0.0029799149570789440488738364365418;0.0027266556835268129788119040313177;0.0024846123172992951033677400118904;0.0022537903176392259929627925885143;0.00203419489069373016221220495936;0.0018258309893965374293145487172296;0.0016287033133565165243794581328984;0.00144281630875153776827346518985;0.001268174168228275444647579206503;0.0011047808308075057759367609833134;0.00095263998179551112599483531084843;0.00081175505270059122864267919794656;0.00068212922115606922091046726563945;0.00056376541084829367989073034550529;0.00045666629145085790852931495464873;0.00036083427856448135884193106903695;0.00027627153366222012564890064822976;0.00020297996404095020039903829456307;0.00014096122277840184011665769503452;9.0216708695634029169241330237128e-05;5.0747566325726189973011059919372e-05;2.2554685887743453065468202112243e-05;5.6387032669191761158344888826832e-06],dataType);props.OverlapLength = cast(882,dataType); props.SampleRate = cast(44100,dataType); props.FFTLength = uint16(1323); props.NumFeatures = uint8(41); end function [config, outputIndex] = getConfig(dataType, props) powerNormalizationFactor = 1/(sum(props.Window)^2); config.OneSidedSpectrumBins = uint16(1:662); linearSpectrumFrequencyBins = 1:662; config.linearSpectrum.FrequencyBins = uint16(linearSpectrumFrequencyBins); config.linearSpectrum.NormalizationFactor = cast(2*powerNormalizationFactor,dataType); melFilterbank = designAuditoryFilterBank(props.SampleRate, ... FrequencyScale="mel", ... MelStyle="oshaughnessy", ... FFTLength=props.FFTLength, ... OneSided=true, ... FrequencyRange=[0 22050], ... NumBands=32, ... Normalization="bandwidth", ... FilterBankDesignDomain="linear"); melFilterbank = melFilterbank*powerNormalizationFactor; config.melSpectrum.FilterBank = cast(melFilterbank,dataType); FFTLength = cast(props.FFTLength,like=props.SampleRate); w = (props.SampleRate/FFTLength)*(linearSpectrumFrequencyBins-1); w(end) = props.SampleRate*(FFTLength-1)/(2*FFTLength); config.SpectralDescriptorInput.FrequencyVector = cast(w(:),dataType); outputIndex.mfcc = uint8(1:13); outputIndex.mfccDelta = uint8(14:26); outputIndex.mfccDeltaDelta = uint8(27:39); outputIndex.spectralCentroid = uint8(40); outputIndex.pitch = uint8(41); end function state = getState(dataType, numChannels) state.NumChannels = numChannels; state.mfccDelta = zeros(8,13,numChannels,dataType); state.mfccDeltaDelta = zeros(8,13,numChannels,dataType); end function state = reset(state) state.mfccDelta(:,:,:) = 0; state.mfccDeltaDelta(:,:,:) = 0; end function y = applyFilterBank(filterBank, Z, dataType, varargin) if isempty(coder.target) y = filterBank*Z; else % Generate optimized C/C++ code for filter bank operation [numBands,filterLength] = size(filterBank); numChan = size(Z,2); if nargin == 3 y = zeros(numBands,numChan,dataType); else y = varargin{1}; end for channel = 1:numChan temp = zeros(numBands,1,dataType); for jj = 1:filterLength temp = temp + Z(jj,channel)*filterBank(:,jj); end y(:,channel) = temp; end end end
The generated function contains help text that indicates any requirements on the input. In this example, the sample rate of the input should be 44.1 kHz, the frame input to the function should be 1323 samples, and successive frames should be overlapped by 882 samples before calling the function. The differences between the audioFeatureExtractor
object and the function are described in more detail in Approximate Equivalency Between audioFeatureExtractor and Generated Function.
help extractAudioFeatures
extractAudioFeatures Extract multiple features from streaming audio featureVector = extractAudioFeatures(audioIn) returns audio features extracted from audioIn. featureVector = extractAudioFeatures(audioIn,Reset=TF) returns feature extractors to their initial conditions before extracting features. Parameters of the audioFeatureExtractor used to generate this function must be honored when calling this function. - Sample rate of the input should be 44100 Hz. - Frame length of the input should be 1323 samples. - Successive frames of the input should be overlapped by 882 samples before calling extractAudioFeatures. % Example 1: Extract features source = dsp.ColoredNoise(); inputBuffer = dsp.AsyncBuffer; for ii = 1:10 audioIn = source(); write(inputBuffer,audioIn); while inputBuffer.NumUnreadSamples > 441 x = read(inputBuffer,1323,882); featureVector = extractAudioFeatures(x); % ... do something with featureVector ... end end % Example 2: Extract features from speech regions only [audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav"); audioIn = resample(audioIn,44100,fs); source = dsp.AsyncBuffer(size(audioIn,1)); write(source,audioIn); TF = false; while source.NumUnreadSamples > 441 x = read(source,1323,882); isSilence = var(x) < 0.01; if ~isSilence featureVector = extractAudioFeatures(x,Reset=TF); TF = false; else TF = true; end % ... do something with featureVector ... end % Example 3: Generate code that does not use reset targetDataType = "single"; codegen extractAudioFeatures -args {ones(1323,1,targetDataType)} source = dsp.ColoredNoise(OutputDataType=targetDataType); inputBuffer = dsp.AsyncBuffer; for ii = 1:10 audioIn = source(); write(inputBuffer,audioIn); while inputBuffer.NumUnreadSamples > 441 x = read(inputBuffer,1323,882); featureVector = extractAudioFeatures_mex(x); % ... do something with featureVector ... end end % Example 4: Generate code that uses reset targetDataType = "single"; codegen extractAudioFeatures -args {ones(1323,1,targetDataType),"Reset",true} [audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav"); audioIn = resample(audioIn,44100,fs); source = dsp.AsyncBuffer(size(audioIn,1)); write(source,cast(audioIn,targetDataType)); TF = false; while source.NumUnreadSamples > 441 x = read(source,1323,882); isSilence = var(x) < 0.01; if ~isSilence featureVector = extractAudioFeatures_mex(x,Reset=TF); TF = false; else TF = true; end % ... do something with featureVector ... end See also audioFeatureExtractor, dsp.AsyncBuffer, codegen.
The examples in the help show how to use the function directly in MATLAB and how to generate C/C++ code. Run the first example to see how to use the function to extract features in MATLAB.
source = dsp.ColoredNoise(); inputBuffer = dsp.AsyncBuffer; for ii = 1:10 audioIn = source(); write(inputBuffer,audioIn); while inputBuffer.NumUnreadSamples > 441 x = read(inputBuffer,1323,882); featureVector = extractAudioFeatures(x); % ... do something with featureVector ... end end
Run the second example to see how to extract features in MATLAB while using the optional "Reset"
name-value pair. The Reset
name-value pair enables you to reset states on the function. For example, if you are only concerned with extracting features from regions of voiced speech and want to avoid the overhead of extracting features constantly, you can use the "Reset"
parameter to avoid bleeding feature information between regions.
[audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav"); source = dsp.AsyncBuffer(size(audioIn,1)); write(source,audioIn); TF = false; while source.NumUnreadSamples > 441 x = read(source,1323,882); isSilence = var(x) < 0.01; if ~isSilence featureVector = extractAudioFeatures(x,"Reset",TF); TF = false; else TF = true; end % ... do something with featureVector ... end
Run the third example to see how to generate code that does not include the ability to reset state. When generating code that does not use the 'Reset'
parameter, only specify a prototype for the audio input argument. The following code requires MATLAB Coder™.
targetDataType = "single"; codegen extractAudioFeatures -args {ones(1323,1,targetDataType)}
Code generation successful.
source = dsp.ColoredNoise('OutputDataType',targetDataType); inputBuffer = dsp.AsyncBuffer; for ii = 1:10 audioIn = source(); write(inputBuffer,audioIn); while inputBuffer.NumUnreadSamples > 441 x = read(inputBuffer,1323,882); featureVector = extractAudioFeatures_mex(x); % ... do something with featureVector ... end end
Run the fourth example to see how to generate code that can reset state. When generating code that uses the 'Reset'
parameter, specify prototype input arguments for the full function signature. The following code requires MATLAB Coder™.
targetDataType = "single"; codegen extractAudioFeatures -args {ones(1323,1,targetDataType),'Reset',true}
Code generation successful.
[audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav"); source = dsp.AsyncBuffer(size(audioIn,1)); write(source,cast(audioIn,targetDataType)); TF = false; while source.NumUnreadSamples > 441 x = read(source,1323,882); isSilence = var(x) < 0.01; if ~isSilence featureVector = extractAudioFeatures_mex(x,'Reset',TF); TF = false; else TF = true; end % ... do something with featureVector ... end
Approximate Equivalency Between audioFeatureExtractor
and Generated Function
When you call extract
using audioFeatureExtractor
, the input is buffered internally prior to feature extraction. The output from extract
is an L-by-M-by-N array, where L is the number of feature vectors and is equal to the number of analysis windows. M is the number of features extracted per analysis window. N is the number of channels.
featuresA = extract(afe,audioToVerify); [L,M,N] = size(featuresA)
L = 1551
M = 41
N = 1
When you call the generated function, extractAudioFeatures, the input should represent a single frame of audio data. The output from the generated function is an M-by-N matrix, where M is the number of features extracted and N is the number of channels. Use the generated function to extract features from the audio signal audioIn
. Use the dsp.AsyncBuffer
object to buffer the input into the required frame length and overlap length prior to calling extractAudioFeatures. Reshape the extracted feature vectors to match the orientation output from audioFeatureExtractor
.
frameLength = 1323; overlapLength = 882; hopLength = frameLength - overlapLength; featuresB = zeros(L,M,N); buff = dsp.AsyncBuffer('Capacity',numel(audioToVerify)); write(buff,audioToVerify); hop = 1; while buff.NumUnreadSamples > hopLength if hop==1 x = read(buff,frameLength); features = extractAudioFeatures(x,'Reset',true); else x = read(buff,frameLength,overlapLength); features = extractAudioFeatures(x); end featuresB(hop,:,:) = reshape(features,[1,M,N]); hop = hop + 1; end
Visualize the difference between the output from audioFeatureExtractor
and the generated function. The differences between frames are less than 1.8e-14
and are due to the different code paths being optimized for batch versus stream processing.
differenceBetweenFrames = sum(abs(featuresA-featuresB),2); plot(differenceBetweenFrames) xlabel('Frame') title('Absolute Difference Between Feature Vectors')
Input Arguments
afe
— Input object
audioFeatureExtractor
object
Input object, specified as an audioFeatureExtractor
object.
fileName
— File name
character vector | string scalar
File name where the generated function is saved, specified as a character vector or string scalar.
Data Types: char
| string
TF
— Flag to specify if function is for streaming
false
(default) | true
Flag to specify if generated function is intended for stream processing, specified
as true
or false
.
Data Types: logical
Version History
Introduced in R2020b
See Also
codegen
(MATLAB Coder) | dsp.AsyncBuffer
| audioFeatureExtractor
| vggishEmbeddings
Commande MATLAB
Vous avez cliqué sur un lien qui correspond à cette commande MATLAB :
Pour exécuter la commande, saisissez-la dans la fenêtre de commande de MATLAB. Les navigateurs web ne supportent pas les commandes MATLAB.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)