Need Help about FFT and STFT

Hi!

I got a large amount of data, more than 5mb, so I can’t upload it. I would like to ask, my data is three xyz three-axis data collected from acceleratoter and it based on time, they are written in a .mat file.

I want to intercept a small part of the time from this .mat file. What should I do?

After that when i get the new data from that time ,how can i calculate the FFT Power Spectrum for a sliding window ? Can someone help me with this? Best Regards!

Answer 1

[Mathieu NOE]

hello

see the code below for (averaged) fft analysis and spectrogram

you can easily incorporate a test to select samples that matches the condition time > t_min and time < t_max.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

load('signal15.mat') % time (tout) and data (simout)
% t = tout;
channel = 1;
signal = simout(:,channel);
samples = length(signal);
Fs = 1/mean(diff(tout));

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 4096;    % 
OVERLAP = 0.75;

% spectrogram dB scale
spectrogram_dB_scale = 80;  % dB range scale (means , the lowest displayed level is XX dB below the max level)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% if you are dealing with acoustics, you may wish to have A weighted
% spectrums 

% option_w = 0 : linear spectrum (no weighting dB (L) )
% option_w = 1 : A weighted spectrum (dB (A) )
option_w = 0;

%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 2;
if decim>1
    signal = decimate(signal,decim);
    Fs = Fs/decim;
end

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 1 : averaged FFT spectrum
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[freq, sensor_spectrum] = myfft_peak(signal,Fs,NFFT,OVERLAP);

% convert to dB scale (ref = 1)
sensor_spectrum_dB = 20*log10(sensor_spectrum);

% apply A weigthing if needed
if option_w == 1
    pondA_dB = pondA_function(freq);
    sensor_spectrum_dB = sensor_spectrum_dB+pondA_dB;
    my_ylabel = ('Amplitude (dB (A))');
else
    my_ylabel = ('Amplitude (dB (L))');
end


figure(1),plot(freq,sensor_spectrum_dB,'b');grid
title(['Averaged FFT Spectrum  / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(freq(2)-freq(1)) ' Hz ']);
xlabel('Frequency (Hz)');ylabel(my_ylabel);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

[sg,fsg,tsg] = specgram(signal,NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));  

% FFT normalisation and conversion amplitude from linear to dB (peak)
sg_dBpeak = 20*log10(abs(sg))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only

% apply A weigthing if needed
if option_w == 1
    pondA_dB = pondA_function(fsg);
    sg_dBpeak = sg_dBpeak+(pondA_dB*ones(1,size(sg_dBpeak,2)));
    my_title = ('Spectrogram (dB (A))');
else
    my_title = ('Spectrogram (dB (L))');
end

% saturation of the dB range : 
% saturation_dB = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
min_disp_dB = round(max(max(sg_dBpeak))) - spectrogram_dB_scale;
sg_dBpeak(sg_dBpeak<min_disp_dB) = min_disp_dB;

% plots spectrogram
figure(2);
imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([my_title ' / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');




function pondA_dB = pondA_function(f)
	% dB (A) weighting curve
	n = ((12200^2*f.^4)./((f.^2+20.6^2).*(f.^2+12200^2).*sqrt(f.^2+107.7^2).*sqrt(f.^2+737.9^2)));
	r = ((12200^2*1000.^4)./((1000.^2+20.6^2).*(1000.^2+12200^2).*sqrt(1000.^2+107.7^2).*sqrt(1000.^2+737.9^2))) * ones(size(f));
	pondA = n./r;
	pondA_dB = 20*log10(pondA(:));
end

function  [freq_vector,fft_spectrum] = myfft_peak(signal, Fs, nfft, Overlap)
% FFT peak spectrum of signal  (example sinus amplitude 1   = 0 dB after fft).
% Linear averaging
%   signal - input signal, 
%   Fs - Sampling frequency (Hz).
%   nfft - FFT window size
%   Overlap - buffer overlap % (between 0 and 0.95)
signal = signal(:);
samples = length(signal);
% fill signal with zeros if its length is lower than nfft
if samples<nfft
    s_tmp = zeros(nfft,1);
    s_tmp((1:samples)) = signal;
    signal = s_tmp;
    samples = nfft;
end

% window : hanning
window = hanning(nfft);
window = window(:);

%    compute fft with overlap 
 offset = fix((1-Overlap)*nfft);
 spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
%     % for info is equivalent to : 
%     noverlap = Overlap*nfft;
%     spectnum = fix((samples-noverlap)/(nfft-noverlap));	% Number of windows

    % main loop
    fft_spectrum = 0;
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft)).*window;
        fft_spectrum = fft_spectrum + (abs(fft(sw))*4/nfft);     % X=fft(x.*hanning(N))*4/N; % hanning only 
    end
    fft_spectrum = fft_spectrum/spectnum; % to do linear averaging scaling

% one sidded fft spectrum  % Select first half 
    if rem(nfft,2)    % nfft odd
        select = (1:(nfft+1)/2)';
    else
        select = (1:nfft/2+1)';
    end
fft_spectrum = fft_spectrum(select);
freq_vector = (select - 1)*Fs/nfft;
end 

[Xiaoming Hu]

Thanks for your Answer. I would like to ask. I have finisched(below) the step of calculate the fft windows. Now i want to calculate the average, the mean of all windows. What should i do?

clc;clear all;close all;
load('UPDRS_ACC_DATA.mat')

time_vec = 1/Fs:1/Fs:size(ACC_DATA_R,2)/Fs;
time_postural_tremor  = 103050:1:151900; % second 25-37
xL = ACC_DATA_L(:,time_postural_tremor)';
xR = ACC_DATA_R(:,time_postural_tremor);



%caculate fft with window 
%left
windowsize = Fs*2; %because the window is 2s , and sample frequncy is 4096, so it is the size
window = hamming(windowsize); 
nfft = windowsize; %equal to window size
noverlap = Fs; % overlap is 1s,so it is Fs
xL1 = ACC_DATA_L(3,time_postural_tremor);%tremor data is z axis used
[S1,F1,T1] = spectrogram(xL1,window,noverlap,nfft,Fs);
imagesc(T1, F1, 20*log10((abs(S1))));xlabel('Time in S LEFT'); ylabel('Freqency');
colorbar;


%right
windowsize = Fs*2; %because the window is 2s , and sample frequncy is 4096, so it is the size
window = hamming(windowsize); 
nfft = windowsize; %equal to window size
noverlap = Fs; % overlap is 1s,so it is Fs
xR1 = ACC_DATA_R(3,time_postural_tremor);%tremor data is z axis used
[S2,F2,T2] = spectrogram(xR1,window,noverlap,nfft,Fs);
figure; 
imagesc(T2, F2, 20*log10((abs(S2))));xlabel('Time in s RIGHT'); ylabel('Freqency');
colorbar;
%why i can not show the right and left spectrum the same time?as you see it
%is only right
% Answer: you need to open new "figure" (I added it in line 30); otherwise the plot
% is overwritten

figure
% raw data
subplot(2,1,1);
plot(time_vec(time_postural_tremor), xL); 
title('Postural Tremor LEFT')
ylabel('Acceleration (raw data)')
xlabel('Time in s')
xlim([time_vec(time_postural_tremor(1)) time_vec(time_postural_tremor(end))])
legend({'x','y','z'})
grid on
subplot(2,1,2);
plot(time_vec(time_postural_tremor), xR); 
title('Postural Tremor RIGHT')
ylabel('Acceleration (raw data)')
xlabel('Time in s')
xlim([time_vec(time_postural_tremor(1)) time_vec(time_postural_tremor(end))])
legend({'x','y','z'})
grid on

[Mathieu NOE]

hello

for example , you can average S1 along the time axis to get only a vector , that must have the same length as F1.

[Xiaoming Hu]

thanks ！ one more question:

will the window lengths and overlaps influences the outcome ? How can i select a good size of window?

[Mathieu NOE]

hello

If your window lenghth is nfft , the spectrum frequency resolution is df = Fs/nfft ; so there are compromise between frequency resolution and time resolution for a spectrogram plot.

I usually start with an overlap of 50 to 75% of nfft .

if I really need to heave a smoother and refined time resolution , I can go up to 95 / 97% of overlap.

[Xiaoming Hu]

Thanks Professor!!! HHH,

I have finisch the nfft and i just get the area what i want to use from 0.9hz to 15hz. Then i want to get a root mean square value. The code what i have did till right now is below.

windowsize = Fs*2; %because the window is 2s , and sample frequncy is 4096, so it is the size
window = hamming(windowsize); 
nfft = windowsize; %equal to window size
noverlap = Fs; % overlap is 1s,so it is Fs
xR2 = ACC_DATA_R(3,time_postural_tremor);%tremor data is z axis used
[S2,F2,T2,P2] = spectrogram(xR2,window,noverlap,nfft,Fs);%%this is for calculate the average power

f_bigger_09Hz = find(F2>0.9,1,'first');
f_15Hz = find(F2<=15,1,'last');
%Right
figure;
plot(F2(f_bigger_09Hz:f_15Hz),P2(f_bigger_09Hz:f_15Hz,:))
ylabel('power')
xlabel('Frequency in Hz right')
grid on
%Left
figure;
plot(F1(f_bigger_09Hz:f_15Hz),P1(f_bigger_09Hz:f_15Hz,:))
ylabel('power')
xlabel('Frequency in Hz left')
grid on  %% iget the area what i need(0.9hz to 15h

Can u give me a help how to calculate this area to get a root mean square value?

Thanks!