# mfcc

Extract MFCC, log energy, delta, and delta-delta of audio signal

## Description

example

coeffs = mfcc(audioIn,fs) returns the mel frequency cepstral coefficients (MFCCs) for the audio input, sampled at a frequency of fs Hz.

coeffs = mfcc(___,Name,Value) specifies options using one or more Name,Value pair arguments.

Example: coeffs = mfcc(audioIn,fs,'LogEnergy','Replace') returns mel frequency cepstral coefficients for the audio input signal sampled at fs Hz. The first coefficient in the coeffs vector is replaced with the log energy value.

[coeffs,delta,deltaDelta,loc] = mfcc(___) also returns the delta, delta-delta, and location of samples corresponding to each window of data.

## Examples

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Compute the mel frequency cepstral coefficients of a speech signal using the mfcc function. The function returns delta, the change in coefficients, and deltaDelta, the change in delta values. The log energy value that the function computes can prepend the coefficients vector or replace the first element of the coefficients vector. This is done based on whether you set the 'LogEnergy' argument to 'Append' or 'Replace'.

Read an audio signal from the 'Counting-16-44p1-mono-15secs.wav' file using the audioread function. The mfcc function processes the entire speech data in a batch. Based on the number of input rows, the window length, and the overlap length, mfcc partitions the speech into 1551 frames and computes the cepstral features for each frame. Each row in the coeffs matrix corresponds to the log-energy value followed by the 13 mel-frequency cepstral coefficients for the corresponding frame of the speech file. The function also computes loc, the location of the last sample in each input frame.

Read in an audio file and convert it to a frequency representation.

win = hann(1024,"periodic");
S = stft(audioIn,"Window",win,"OverlapLength",512,"Centered",false);

To extract the mel-frequency cepstral coefficients, call mfcc with the frequency-domain audio. Ignore the log-energy.

coeffs = mfcc(S,fs,"LogEnergy","Ignore");

In many applications, MFCC observations are converted to summary statistics for use in classification tasks. Plot a probability density function for one of the mel-frequency cepstral coefficients to observe its distributions.

nbins = 60;
coefficientToAnalyze = 4;

histogram(coeffs(:,coefficientToAnalyze+1),nbins,"Normalization","pdf")
title(sprintf("Coefficient %d",coefficientToAnalyze))

## Input Arguments

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Input signal, specified as a vector, matrix, or 3-D array.

• If 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.

• If audioIn is complex, it is interpreted as a frequency-domain signal. In this case, audioIn must be an L-by-M-by-N array, where L is the number of DFT points, M is the number of individual spectrums, and N is the number of individual channels.

Data Types: single | double
Complex Number Support: Yes

Sample rate of the input signal in Hz, specified as a positive scalar.

Data Types: single | double

### Name-Value Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is 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 Name1,Value1,...,NameN,ValueN.

Example: [coeffs,delta,deltaDelta,loc] = mfcc(audioIn,fs,'LogEnergy','Replace','DeltaWindowLength',5) returns mel frequency cepstral coefficients for the audio input signal sampled at fs Hz. The first coefficient in the coeffs vector is replaced with the log energy value. A set of 5 cepstral coefficients is used to compute the delta and the delta-delta values.

Window applied in time domain, specified as the comma-separated pair consisting of 'Window' and a real vector. The number of elements in the vector must be in the range [1,size(audioIn,1)]. The number of elements in the vector must also be greater than OverlapLength.

Data Types: single | double

Number of samples overlapped between adjacent windows, specified as the comma-separated pair consisting of 'OverlapLength' and an integer in the range [0, numel(Window)). If unspecified, OverlapLength defaults to round(0.02*fs).

Data Types: single | double

Number of coefficients returned for each window of data, specified as an integer in the range [2 v], where v is the number of valid passbands.

The number of valid passbands is defined as sum(BandEdges <= floor(fs/2))-2. A passband is valid if its edges fall below fs/2, where fs is the sample rate of the input audio signal, specified as the second argument, fs.

Data Types: single | double

Band edges of the filter bank in Hz, specified as a nonnegative monotonically increasing row vector in the range [0, fs/2]. The number of band edges must be in the range [4, 160]. The mfcc function designs half-overlapped triangular filters based on BandEdges. This means that all band edges, except for the first and last, are also center frequencies of the designed bandpass filters.

By default, BandEdges is a 42-element vector, which results in a 40-band filter bank that spans approximately 133 Hz to 6864 Hz. The default bands are spaced as described in [2].

Data Types: single | double

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 in the Window.

Data Types: single | double

Type of nonlinear rectification applied prior to the discrete cosine transform, specified as 'log' or 'cubic-root'.

Data Types: char | string

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 unspecified, DeltaWindowLength defaults to 9.

Deltas are computed using the audioDelta function.

Data Types: single | double

Specify how the log energy is shown in the coefficients vector output, specified as:

• 'Append' –– The function prepends the log energy to the coefficients vector. The length of the coefficients vector is 1 + NumCoeffs.

• 'Replace' –– The function replaces the first coefficient with the log energy of the signal. The length of the coefficients vector is NumCoeffs.

• 'Ignore' –– The object does not calculate or return the log energy.

Data Types: char | string

## Output Arguments

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Mel frequency 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, Window, and OverlapLength control this dimension: L = floor((size(audioIn,1) − numel(Window)))/(numel(Window)OverlapLength) + 1.

• M –– Number of coefficients returned per frame. This value is determined by NumCoeffs and LogEnergy.

When LogEnergy is set to:

• 'Append' –– The function prepends the log energy value to the coefficients vector. The length of the coefficients vector is 1 + NumCoeffs.

• 'Replace' –– The function replaces the first coefficient with the log energy of the signal. The length of the coefficients vector is NumCoeffs.

• 'Ignore' –– The function does not calculate or return the log energy. The length of the coefficients vector is NumCoeffs.

• N –– Number of input channels (columns). This value is size(audioIn,2).

Data Types: single | double

Change in coefficients from one frame of data 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.

Data Types: single | double

Change in delta values from one frame of data to another, returned as an L-by-M matrix or an L-by-M-by-N array. The deltaDelta array is the same size and data type as the coeffs and delta arrays.

Data Types: single | double

Location of last sample in each analysis window, returned as a column vector with the same number of rows as coeffs.

Data Types: single | double

## Algorithms

Mel frequency 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 mel frequency 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 mel filter bank linearly spaces the first 10 triangular filters and logarithmically spaces the remaining filters.

The information contained in the zeroth mel frequency cepstral coefficient is often augmented with or replaced by the log energy. The log energy calculation depends on the input domain.

If the input (audioIn) is a time-domain signal, the log energy is computed using the following equation:

$\mathrm{log}E=\mathrm{log}\left(\text{sum}\left({x}^{2}\right)\right)$

If the input (audioIn) is a frequency-domain signal, the log energy is computed using the following equation:

$\mathrm{log}E=\mathrm{log}\left(\text{sum}\left({|x|}^{2}\right)/FFTLength\right)$

## Compatibility Considerations

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Behavior changed in R2020b

Behavior change in future release

## References

[1] Rabiner, Lawrence R., and Ronald W. Schafer. Theory and Applications of Digital Speech Processing. Upper Saddle River, NJ: Pearson, 2010.

## Extended Capabilities

### GPU ArraysAccelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

Introduced in R2018a

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