cepstralCoefficients
Extract cepstral coefficients
Description
specifies options using one or more coeffs
= cepstralCoefficients(S
,Name,Value
)Name,Value
pair arguments.
For example, coeffs =
cepstralCoefficients(S,'Rectification','cubic-root')
uses cubic-root
rectification to calculate the coefficients.
Examples
Mel Frequency Cepstral Coefficients
Read an audio file into the workspace.
[audioIn,fs] = audioread('SpeechDFT-16-8-mono-5secs.wav');
Convert the audio signal to a frequency-domain representation using 30 ms windows with 15 ms overlap. Because the input is real and therefore the spectrum is symmetric, you can use just one side of the frequency domain representation without any loss of information. Convert the complex spectrum to the magnitude spectrum: phase information is discarded when calculating mel frequency cepstral coefficients (MFCC).
windowLength = round(0.03*fs); overlapLength = round(0.015*fs); S = stft(audioIn,"Window",hann(windowLength,"periodic"),"OverlapLength",overlapLength,"FrequencyRange","onesided"); S = abs(S);
Design a one-sided frequency-domain mel filter bank. Apply the filter bank to the frequency-domain representation to create a mel spectrogram.
filterBank = designAuditoryFilterBank(fs,'FFTLength',windowLength);
melSpec = filterBank*S;
Call cepstralCofficients
with the mel spectrogram to create MFCC.
melcc = cepstralCoefficients(melSpec);
Gammatone Frequency Cepstral Coefficients
Read an audio signal and convert it to a one-sided magnitude short-time Fourier transform. Use a 50 ms periodic Hamming window with a 10 ms hop.
[audioIn,fs] = audioread('NoisySpeech-16-22p5-mono-5secs.wav'); windowLength = round(0.05*fs); hopLength = round(0.01*fs); overlapLength = windowLength - hopLength; S = stft(audioIn,"Window",hamming(windowLength,'periodic'),"OverlapLength",overlapLength,"FrequencyRange","onesided"); S = abs(S);
Design a one-sided frequency-domain gammatone filter bank. Apply the filter bank to the frequency-domain representation to create a gammatone spectrogram.
filterBank = designAuditoryFilterBank(fs,'FFTLength',windowLength,"FrequencyScale","erb"); gammaSpec = filterBank*S;
Call cepstralCoefficients
with the gammatone spectrogram to create gammatone frequency cepstral coefficients. Use a cubic-root rectification.
gammacc = cepstralCoefficients(gammaSpec,"Rectification","cubic-root");
Custom Cepstral Coefficients
Cepstral coefficients are commonly used as compact representations of audio signals. Generally, they are calculated after an audio signal is passed through a filter bank and the energy in the individual filters is summed. Researchers have proposed various filter banks based on psychoacoustic experiments (such as mel, Bark, and ERB). Using the cepstralCoefficients
function, you can define your own custom filter bank and then analyze the resulting cepstral coefficients.
Read in an audio file for analysis.
[audioIn,fs] = audioread('Counting-16-44p1-mono-15secs.wav');
Design a filter bank that consists of 20 triangular filters with band edges over the range 62.5 Hz to 8000 Hz. Spread the filters evenly in the log domain. For simplicity, design the filters in bins. Most popular auditory filter banks are designed in a continuous domain, such as Hz, mel, or Bark, and then warped back to bins.
numFilters =20; filterbankStart =
62.5; filterbankEnd =
8000; numBandEdges = numFilters + 2; NFFT = 1024; filterBank = zeros(numFilters,NFFT); bandEdges = logspace(log10(filterbankStart),log10(filterbankEnd),numBandEdges); bandEdgesBins = round((bandEdges/fs)*NFFT) + 1; for ii = 1:numFilters filt = triang(bandEdgesBins(ii+2)-bandEdgesBins(ii)); leftPad = bandEdgesBins(ii); rightPad = NFFT - numel(filt) - leftPad; filterBank(ii,:) = [zeros(1,leftPad),filt',zeros(1,rightPad)]; end
Plot the filter bank.
frequencyVector = (fs/NFFT)*(0:NFFT-1);
plot(frequencyVector,filterBank');
xlabel('Hz')
axis([0 frequencyVector(NFFT/2) 0 1])
Transform the audio signal using the stft
function, and then apply the custom filter bank. Apply the filter bank to the frequency-domain representation to create a custom auditory spectrogram. Plot the spectrogram.
[S,~,t] = stft(audioIn,fs,"Window",hann(NFFT,'periodic'),"FrequencyRange","twosided"); S = abs(S); spec = filterBank*S; surf(t,bandEdges(2:end-1),10*log10(spec),'EdgeColor','none') view([0,90]) axis([t(1) t(end) bandEdges(2) bandEdges(end-1)]) xlabel('Time (s)') ylabel('Frequency (Hz)') c = colorbar; c.Label.String = 'Power (dB)';
Call cepstralCoefficients
with the custom auditory spectrogram to create custom cepstral coefficients.
ccc = cepstralCoefficients(S);
Extract Cepstral Coefficients from Streaming Audio
Create a dsp.AudioFileReader
object to read in audio frame-by-frame. Create a dsp.AsyncBuffer
object to buffer the input into overlapped frames.
fileReader = dsp.AudioFileReader("Ambiance-16-44p1-mono-12secs.wav");
buff = dsp.AsyncBuffer;
Design a two-sided mel filter bank that is compatible with 30 ms windows.
windowLength = round(0.03*fileReader.SampleRate); filterBank = designAuditoryFilterBank(fileReader.SampleRate,"FFTLength",windowLength,"OneSided",false);
In an audio stream loop:
Read a frame of data from the audio file.
Write the frame of data to the buffer.
If enough data is available for a hop, read a 30 ms frame of data from the buffer with a 20 ms overlap between frames.
Transform the data to a magnitude spectrum.
Apply the mel filter bank to create a mel spectrum.
Call
cepstralCoefficients
to return the mel frequency cepstral coefficients (MFCC).
win = hann(windowLength,'periodic'); overlapLength = round(0.02*fileReader.SampleRate); hopLength = windowLength - overlapLength; while ~isDone(fileReader) audioIn = fileReader(); write(buff,audioIn); while buff.NumUnreadSamples > hopLength x = read(buff,windowLength,overlapLength); X = abs(fft(x.*win)); melSpectrum = filterBank*X; melcc = cepstralCoefficients(melSpectrum); end end
Input Arguments
S
— Spectrogram or auditory spectrogram
matrix | 3-D array
Spectrogram or auditory spectrogram, specified as an L-by-M matrix or L-by-M-by-N 3-D array, where:
L –– Number of frequency bands
M –– Number of frames
N –– Number of channels
Data Types: single
| double
Name-Value Arguments
Specify optional pairs of arguments as
Name1=Value1,...,NameN=ValueN
, where Name
is
the argument name and Value
is the corresponding value.
Name-value arguments must appear after other arguments, but the order of the
pairs does not matter.
Before R2021a, use commas to separate each name and value, and enclose
Name
in quotes.
Example: 'NumCoeffs',16
NumCoeffs
— Number of cepstral coefficients returned
13
(default) | positive integer greater than one
Number of coefficients returned for each window of data, specified as the
comma-separated pair consisting of 'NumCoeffs'
and a positive
integer greater than one.
Data Types: single
| double
| int8
| int16
| int32
| int64
| uint8
| uint16
| uint32
| uint64
Rectification
— Type of nonlinear rectification
'log'
(default) | 'cubic-root'
| 'none'
Type of nonlinear rectification applied prior to the discrete cosine transform,
specified as the comma-separated pair consisting of 'Rectification'
and 'log'
, 'cubic-root'
, or
'none'
.
Data Types: char
| string
Output Arguments
coeffs
— Cepstral coefficients
matrix | 3-D array
Cepstral coefficients, returned as an M-by-B matrix or M-by-B-by-N array, where:
M –– Number of frames (columns) of the input.
B –– Number of coefficients returned per frame. This is determined by
NumCoeffs
.N –– Number of channels (pages) of the input.
Data Types: single
| double
Algorithms
Given a time-frequency representation, the cepstralCoefficients
function performs the following operations on each spectrum, individually, as described in
[1]:
Rectifies the spectrum by applying a logarithm or cubic-root, as specified by the
Rectification
parameter.Transforms the rectified spectrum using the DCT-II transform.
Returns the first
NumCoeffs
from the cepstral representation.
References
[1] Rabiner, Lawrence R., and Ronald W. Schafer. Theory and Applications of Digital Speech Processing. Upper Saddle River, NJ: Pearson, 2010.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.
GPU Arrays
Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.
Version History
See Also
mfcc
| gtcc
| audioDelta
| designAuditoryFilterBank
| melSpectrogram
| audioFeatureExtractor
| stft
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