Extract gammatone cepstral coefficients, log-energy, delta, and delta-delta
Get the gammatone cepstral coefficients for an audio file using default settings. Plot the results.
[audioIn,fs] = audioread('Counting-16-44p1-mono-15secs.wav'); [coeffs,~,~,loc] = gtcc(audioIn,fs); t = loc./fs; plot(t,coeffs) xlabel('Time (s)') title('Gammatone Cepstral Coefficients') legend('logE','0','1','2','3','4','5','6','7','8','9','10','11','12', ... 'Location','northeastoutside')
Read in an audio file.
[audioIn,fs] = audioread('Turbine-16-44p1-mono-22secs.wav');
Calculate 20 GTCC using filters equally spaced on the ERB scale between
hz2erb(12000). Calculate the coefficients using 50 ms periodic Hann windows with 25 ms overlap. Replace the 0th coefficient with the log-energy. Use time-domain filtering.
[coeffs,~,~,loc] = gtcc(audioIn,fs, ... 'NumCoeffs',20, ... 'FrequencyRange',[62.5,12000], ... 'Window',hann(round(0.05*fs),'periodic'), ... 'OverlapLength',round(0.025*fs), ... 'LogEnergy','Replace', ... 'FilterDomain','Time');
Plot the results.
t = loc/fs; plot(t,coeffs) xlabel('Time (s)') title('Gammatone Cepstral Coefficients') legend('logE','1','2','3','4','5','6','7','8','9','10','11','12','13', ... '14','15','16','17','18','19','Location','northeastoutside');
Read in an audio file and convert it to a frequency representation.
[audioIn,fs] = audioread("Rainbow-16-8-mono-114secs.wav"); win = hann(1024,"periodic"); S = stft(audioIn,"Window",win,"OverlapLength",512,"Centered",false);
To extract the gammatone cepstral coefficients, call
gtcc with the frequency-domain audio. Ignore the log-energy.
coeffs = gtcc(S,fs,"LogEnergy","Ignore");
In many applications, GTCC observations are converted to summary statistics for use in classification tasks. Plot a probability density function for one of the gammatone cepstral coefficients to observe its distributions.
nbins = 60; coefficientToAnalyze = 4; histogram(coeffs(:,coefficientToAnalyze+1),nbins,'Normalization','pdf') title(sprintf("Coefficient %d",coefficientToAnalyze))
audioIn— Input signal
Input signal, specified as a vector, matrix, or 3-D array.
FilterDomain' is set to
audioIn can be real or complex.
audioIn is real, it is interpreted as a time-domain
signal and must be a column vector or a matrix. Columns of the matrix are treated
as independent audio channels.
audioIn is complex, it is interpreted as a
frequency-domain signal. In this case,
audioIn must be an
where L is the number of DFT points, M is
the number of individual spectra, and N is the number of
FilterDomain' is set to
audioIn must be a real column vector or matrix. Columns of the
matrix are treated as independent audio channels.
Complex Number Support: Yes
fs— Sample rate (Hz)
Sample rate of the input signal in Hz, specified as a positive scalar.
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
coeffs = gtcc(audioIn,fs,'LogEnergy','Replace')returns gammatone cepstral coefficients for the audio input signal sampled at
fsHz. For each analysis window, the first coefficient in the
coeffsvector is replaced with the log energy of the input signal.
Window— Window applied in time domain
hamming(round(fs*0.3),'periodic')(default) | vector
OverlapLength— Number of samples overlapped between adjacent windows
round(0.02*(default) | non-negative scalar
NumCoeffs— Number of coefficients returned
13(default) | positive scalar integer
Number of coefficients returned for each window of data, specified as the
comma-separated pair consisting of
'NumCoeffs' and an integer in
the range [2, v]. v is the number of valid
passbands. If unspecified,
NumCoeffs defaults to
The number of valid passbands is defined as the number of ERB steps
(ERBN) in the frequency range of the filter bank. The
frequency range of the filter bank is specified by
FilterDomain— Domain in which to apply filtering
Domain in which to apply filtering, specified as the comma-separated pair
'Time'. If unspecified,
FrequencyRange— Frequency range of gammatone filter bank (Hz)
[50(default) | two-element row vector
Frequency range of gammatone filter bank in Hz, specified as the comma-separated
pair consisting of
'FrequencyRange' and a two-element row vector of
increasing values in the range [0,
fs/2]. If unspecified,
FrequencyRange defaults to
FFTLength— Number of bins in DFT
numel((default) | positive scalar integer
Number of bins used to calculate the discrete Fourier transform (DFT) of windowed
input samples. The FFT length must be greater than or equal to the number of elements
Rectification— Type of nonlinear rectification
Type of nonlinear rectification applied prior to the discrete cosine transform,
DeltaWindowLength— Number of coefficients used to calculate delta and delta-delta
9(default) | odd integer greater than two
Number of coefficients used to calculate the delta and the delta-delta values,
specified as the comma-separated pair consisting of
'DeltaWindowLength' and an odd integer greater than two. If
DeltaWindowLength defaults to
Deltas are computed using the
LogEnergy— Log energy usage
Log energy usage, specified as the comma-separated pair consisting of
'Ignore'. If unspecified,
LogEnergy defaults to
'Append' –– The function prepends the log energy to the
coefficients vector. The length of the coefficients vector is 1 +
'Replace' –– The function replaces the first coefficient
with the log energy of the signal. The length of the coefficients vector is
'Ignore' –– The function does not calculate or return the
coeffs— Gammatone cepstral coefficients
Gammatone cepstral coefficients, returned as an L-by-M matrix or an L-by-M-by-N array, where:
L –– Number of analysis windows the audio signal is
partitioned into. The input size,
OverlapLength control this dimension:
L = floor((size(.
OverlapLength) + 1
LogEnergy is set to:
'Append' –– The function prepends the log energy
value to the coefficients vector. The length of the coefficients vector is 1
'Replace' –– The function replaces the first
coefficient with the log energy of the signal. The length of the
coefficients vector is
'Ignore' –– The function does not calculate or return
the log energy. The length of the coefficients vector is
N –– Number of input channels (columns). This value is
delta— Change in coefficients
Change in coefficients from one analysis window to another, returned as an
L-by-M matrix or an
L-by-M-by-N array. The
delta array is the same size and data type as the
coeffs array. See
coeffs for the definitions
of L, M, and N.
loc— Location of the last sample in each analysis window
Location of last sample in each analysis window, returned as a column vector with
the same number of rows as
gtcc function splits the entire data into overlapping segments.
The length of each analysis window is determined by
Window. The length of
overlap between analysis windows is determined by
algorithm to determine the gammatone cepstral coefficients depends on the filter domain,
FilterDomain. The default filter domain is frequency.
Gammatone cepstrum coefficients are popular features extracted from speech signals for use in recognition tasks. In the source-filter model of speech, cepstral coefficients are understood to represent the filter (vocal tract). The vocal tract frequency response is relatively smooth, whereas the source of voiced speech can be modeled as an impulse train. As a result, the vocal tract can be estimated by the spectral envelope of a speech segment.
The motivating idea of gammatone cepstral coefficients is to compress information about the vocal tract (smoothed spectrum) into a small number of coefficients based on an understanding of the cochlea. Although there is no hard standard for calculating the coefficients, the basic steps are outlined by the diagram.
The default gammatone filter bank is composed of gammatone filters spaced linearly on
the ERB scale between 50 and 8000 Hz. The filter bank is designed by
The information contained in the zeroth gammatone cepstral coefficient is often augmented with or replaced by the log energy. The log energy calculation depends on the input domain.
If the input is a time-domain signal, the log energy is computed using the following equation:
If the input is a frequency-domain signal, the log energy is computed using the following equation:
FilterDomain is specified as
gtcc function uses the
gammatoneFilterBank to apply time-domain filtering. The basic steps of the
gtcc algorithm are outlined by the diagram.
FrequencyRange and sample rate (
parameters are set on the filter bank using the name-value pairs input to the
gtcc function. The number of filters in the gammatone filter bank is
roughly corresponds to placing a gammatone filter every 0.9 mm in the cochlea.
The output from the gammatone filter bank is a multichannel signal. Each channel output
from the gammatone filter bank is buffered into overlapped analysis windows, as specified by
OverlapLength parameters. The
energy for each analysis window of data is calculated. The STE of the channels are
concatenated. The concatenated signal is then passed through a logarithm function and
transformed to the cepstral domain using a discrete cosine transform (DCT).
The log-energy is calculated on the original audio signal using the same buffering scheme applied to the gammatone filter bank output.
Behavior changed in R2020b
The delta and delta-delta calculations are now computed using the
function, which has a different startup behavior than the previous algorithm. The default
value of the
DeltaWindowLength parameter has changed from
9. A delta window length of
2 is no longer supported.
WindowLengthwill be removed in a future release
Behavior change in future release
WindowLength parameter will be removed from the
gtcc function in a future release. Use the
Window parameter instead.
In releases prior to R2020b, you could only specify the length of a time-domain window. The window was always designed as a periodic Hamming window. You can replace instances of the code
coeffs = gtcc(audioin,fs,'WindowLength',1024);
coeffs = gtcc(audioIn,fs,'Window',hamming(1024,'periodic'));
 Shao, Yang, Zhaozhang Jin, Deliang Wang, and Soundararajan Srinivasan. "An Auditory-Based Feature for Robust Speech Recognition." IEEE International Conference on Acoustics, Speech and Signal Processing. 2009.
 Valero, X., and F. Alias. "Gammatone Cepstral Coefficients: Biologically Inspired Features for Non-Speech Audio Classification." IEEE Transactions on Multimedia. Vol. 14, Issue 6, 2012, pp. 1684–1689.