mfcc

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

Syntax

coeffs = mfcc(audioIn,fs)

coeffs = mfcc(___,Name=Value)

[coeffs,delta,deltaDelta,loc] = mfcc(___)

mfcc(___)

Description

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 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. You can specify an input combination from any of the previous syntaxes.

mfcc(___) with no output arguments plots the mel-frequency cepstral coefficients. Before plotting, the coefficients are normalized to have mean 0 and standard deviation 1.

• If the input is in the time domain, the coefficients are plotted against time.

• If the input is in the frequency domain, the coefficients are plotted against frame number.

• If the log energy is extracted, then it is also plotted.

Examples

Compute Mel Frequency Cepstral Coefficients

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.

[audioIn,fs] = audioread("Counting-16-44p1-mono-15secs.wav");
[coeffs,delta,deltaDelta,loc] = mfcc(audioIn,fs);

Plot the normalized coefficients.

mfcc(audioIn,fs)

Extract MFCC from Frequency-Domain Audio

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 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

audioIn — Input signal

vector | matrix | 3-D array

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 spectra, and N is the number of individual channels.

Data Types: single | double
Complex Number Support: Yes

fs — Sample rate (Hz)

positive scalar

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

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: [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 — Window applied in time domain

hamming(round(0.03*fs),"periodic") (default) | vector

Window applied in time domain, specified as 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

OverlapLength — Number of overlapping samples between adjacent windows

round(fs*0.02) (default) | integer

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

Data Types: single | double

NumCoeffs — Number of coefficients returned

13 (default) | positive scalar integer

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

BandEdges — Band edges of filter bank (Hz)

row vector

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

FFTLength — Number of bins for calculating DFT

numel(Window) (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 in the Window.

Data Types: single | double

Rectification — Type of non-linear rectification

"log" (default) | "cubic-root"

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

Data Types: char | string

DeltaWindowLength — Number of coefficients for calculating delta and delta-delta

9 (default) | odd integer greater than 2

Number of coefficients used to calculate the delta and the delta-delta values, specified as an odd integer greater than two. If unspecified, DeltaWindowLength defaults to 9.

Deltas are computed using the audioDelta function.

Data Types: single | double

LogEnergy — Specify how the log energy is shown

"append" (default) | "replace" | "ignore"

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

coeffs — Mel-frequency cepstral coefficients (MFCCs)

matrix | 3-D array

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

delta — Change in coefficients

matrix | array

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

deltaDelta — Change in delta values

matrix | array

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

loc — Location of the last sample in each input frame

vector

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

MFCC

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.

Log Energy

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:

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

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

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

References

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

[2] Auditory Toolbox. https://engineering.purdue.edu/~malcolm/interval/1998-010/AuditoryToolboxTechReport.pdf

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Code Generation
Generate CUDA® code for NVIDIA® GPUs using GPU Coder™.

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

Version History

Introduced in R2018a

R2020b: Delta and delta-delta computation

The delta and delta-delta calculations are now computed using the audioDelta function, which has a different startup behavior than the previous algorithm. The default value of the DeltaWindowLength parameter has changed from 2 to 9. A delta window length of 2 is no longer supported.

R2020b: WindowLength will be removed in a future release

The WindowLength parameter will be removed from the mfcc 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 = mfcc(audioin,fs,WindowLength=1024);

With this code:

coeffs = mfcc(audioIn,fs,Window=hamming(1024,"periodic"));