# MFCC¶

standard mode | Spectral category

## Inputs¶

`spectrum`

(vector_real) - the audio spectrum

## Outputs¶

`bands`

(vector_real) - the energies in mel bands

`mfcc`

(vector_real) - the mel frequency cepstrum coefficients

## Parameters¶

`dctType`

(integer ∈ [2, 3], default = 2) :the DCT type

`highFrequencyBound`

(real ∈ (0, ∞), default = 11000) :the upper bound of the frequency range [Hz]

`inputSize`

(integer ∈ (1, ∞), default = 1025) :the size of input spectrum

`liftering`

(integer ∈ [0, ∞), default = 0) :the liftering coefficient. Use ‘0’ to bypass it

`logType`

(string ∈ {natural, dbpow, dbamp, log}, default = dbamp) :logarithmic compression type. Use ‘dbpow’ if working with power and ‘dbamp’ if working with magnitudes

`lowFrequencyBound`

(real ∈ [0, ∞), default = 0) :the lower bound of the frequency range [Hz]

`normalize`

(string ∈ {unit_sum, unit_tri, unit_max}, default = unit_sum) :spectrum bin weights to use for each mel band: ‘unit_max’ to make each mel band vertex equal to 1, ‘unit_sum’ to make each mel band area equal to 1 summing the actual weights of spectrum bins, ‘unit_area’ to make each triangle mel band area equal to 1 normalizing the weights of each triangle by its bandwidth

`numberBands`

(integer ∈ [1, ∞), default = 40) :the number of mel-bands in the filter

`numberCoefficients`

(integer ∈ [1, ∞), default = 13) :the number of output mel coefficients

`sampleRate`

(real ∈ (0, ∞), default = 44100) :the sampling rate of the audio signal [Hz]

`silenceThreshold`

(real ∈ (0, ∞), default = 1e-10) :silence threshold for computing log-energy bands

`type`

(string ∈ {magnitude, power}, default = power) :use magnitude or power spectrum

`warpingFormula`

(string ∈ {slaneyMel, htkMel}, default = htkMel) :The scale implementation type: ‘htkMel’ scale from the HTK toolkit [2, 3] (default) or ‘slaneyMel’ scale from the Auditory toolbox [4]

`weighting`

(string ∈ {warping, linear}, default = warping) :type of weighting function for determining triangle area

## Description¶

This algorithm computes the mel-frequency cepstrum coefficients of a spectrum. As there is no standard implementation, the MFCC-FB40 is used by default:

filterbank of 40 bands from 0 to 11000Hz

take the log value of the spectrum energy in each mel band. Bands energy values below silence threshold will be clipped to its value before computing log-energies

DCT of the 40 bands down to 13 mel coefficients

There is a paper describing various MFCC implementations [1].

The parameters of this algorithm can be configured in order to behave like HTK [3] as follows:

type = ‘magnitude’

warpingFormula = ‘htkMel’

weighting = ‘linear’

highFrequencyBound = 8000

numberBands = 26

numberCoefficients = 13

normalize = ‘unit_max’

dctType = 3

logType = ‘log’

liftering = 22

In order to completely behave like HTK the audio signal has to be scaled by 2^15 before the processing and if the Windowing and FrameCutter algorithms are used they should also be configured as follows.

FrameGenerator:

frameSize = 1102

hopSize = 441

startFromZero = True

validFrameThresholdRatio = 1

Windowing:

type = ‘hamming’

size = 1102

zeroPadding = 946

normalized = False

This algorithm depends on the algorithms MelBands and DCT and therefore inherits their parameter restrictions. An exception is thrown if any of these restrictions are not met. The input “spectrum” is passed to the MelBands algorithm and thus imposes MelBands’ input requirements. Exceptions are inherited by MelBands as well as by DCT.

IDCT can be used to compute smoothed Mel Bands. In order to do this:

compute MFCC

smoothedMelBands = 10^(IDCT(MFCC)/20)

Note: The second step assumes that ‘logType’ = ‘dbamp’ was used to compute MFCCs, otherwise that formula should be changed in order to be consistent.

- References:
[1] T. Ganchev, N. Fakotakis, and G. Kokkinakis, “Comparative evaluation of various MFCC implementations on the speaker verification task,” in International Conference on Speach and Computer (SPECOM’05), 2005, vol. 1, pp. 191–194.

[2] Mel-frequency cepstrum - Wikipedia, the free encyclopedia, http://en.wikipedia.org/wiki/Mel_frequency_cepstral_coefficient

[3] Young, S. J., Evermann, G., Gales, M. J. F., Hain, T., Kershaw, D., Liu, X., … Woodland, P. C. (2009). The HTK Book (for HTK Version 3.4). Construction, (July 2000), 384, https://doi.org/http://htk.eng.cam.ac.uk

[4] Slaney, M. Auditory Toolbox: A MATLAB Toolbox for Auditory Modeling Work. Technical Report, version 2, Interval Research Corporation, 1998.

## Source code¶

## See also¶

DCT (standard) DCT (streaming) FrameCutter (standard) FrameCutter (streaming) FrameGenerator (standard) IDCT (standard) IDCT (streaming) MFCC (streaming) MelBands (standard) MelBands (streaming) Windowing (standard) Windowing (streaming)