Dan Ellis : Resources : Matlab :

PLP and RASTA (and MFCC, and inversion) in Matlab
using melfcc.m and invmelfcc.m


One of the first decisions in any pattern recognition system is the choice of what features to use: How exactly to represent the basic signal that is to be classified, in order to make the classification algorithm's job easiest.

Speech recognition is a typical example. Through more than 30 years of recognizer research, many different feature representations of the speech signal have been suggested and tried. The most popular feature representation currently used is the Mel-frequency Cepstral Coefficients or MFCC.

Another popular speech feature representation is known as RASTA-PLP, an acronym for Relative Spectral Transform - Perceptual Linear Prediction. PLP was originally proposed by Hynek Hermansky as a way of warping spectra to minimize the differences between speakers while preserving the important speech information [Herm90]. RASTA is a separate technique that applies a band-pass filter to the energy in each frequency subband in order to smooth over short-term noise variations and to remove any constant offset resulting from static spectral coloration in the speech channel e.g. from a telephone line [HermM94].

RASTA-PLP is implemented in a number of programs, such as the 'rasta' program, and its enhanced version 'feacalc', which are distributed for Unix as part of the SPRACHcore package. In order to understand the algorithm, however, it's useful to have a simple implementation in Matlab. By using Matlab's primitives for FFT calculation, Levinson-Durbin recursion etc., the Matlab code can be made quite small and transparent.

Mike Shire started this implementation in 1997 while he was a graduate student in Morgan's group at ICSI. I have recently revised and extended his implementation to allow both spectral and cepstral outputs, and to allow independent selection of RASTA and/or PLP processing.

This implementation offers only a few control parameters, namely a switch to select or disable rasta filtering, and an option to set the order of PLP modeling (which disables PLP modeling when set to zero). Other important options, such as the basic window and hop sizes, can easily be altered by editing the relevant routines, if desired.


Since Mel-frequency Cepstral Coefficients, the other really popular speech feature, involve almost the same processing steps, I decided to make an implementation for them as well, using the same blocks as far as possible. See below.

Inverting Cepstra to Audio

Sometimes it's interesting to `listen' to what it is that the cepstral representations are really capturing. You can do this, crudely, by recovering the short-time magnitude spectrum implied by the cepstral coefficients, then imposing it on white noise. The routine invmelfcc below does this (actually, it can do it for both MFCC and PLP cepstra, depending on the options you give it).

For more details on reproducing and inverting cepstra from several common feature calculation programs, see the companion page on Reproducing Feature Outputs....


The routines provided here are:

You can download the complete set of routines above as rastamat.tgz (a gzipped tar file).


An example of calculating various speech features is shown below:

 % Load a speech waveform
 [d,sr] = wavread('sm1_cln.wav');
 % Look at its regular spectrogram
 specgram(d, 256, sr);
 % Calculate basic RASTA-PLP cepstra and spectra
 [cep1, spec1] = rastaplp(d, sr);
 % .. and plot them
 imagesc(10*log10(spec1)); % Power spectrum, so dB is 10log10
 axis xy
 axis xy
 % Notice the auditory warping of the frequency axis to give more 
 % space to low frequencies and the way that RASTA filtering 
 % emphasizes the onsets of static sounds like vowels

 % Calculate 12th order PLP features without RASTA
 [cep2, spec2] = rastaplp(d, sr, 0, 12);
 % .. and plot them
 axis xy
 % Notice the greater level of temporal detail compared to the 
 % RASTA-filtered version.  There is also greater spectral detail 
 % because our PLP model order is larger than the default of 8
[rasta and plp spectrograms]
 % Append deltas and double-deltas onto the cepstral vectors
 del = deltas(cep2);
 % Double deltas are deltas applied twice with a shorter window
 ddel = deltas(deltas(cep2,5),5);
 % Composite, 39-element feature vector, just like we use for speech recognition
 cepDpDD = [cep2;del;ddel];

This example calculates 20th order MFCC features (as close as I can get it to the features we distribute for the uspop2002 Music IR dataset) and then turns them back into audio - pretty weird sounding!

 % Read in an mp3 file, downsampled to 22 kHz mono
 [d,sr] = mp3read('thompson_twins--Into_The_Gap--Hold_Me_Now--3.mp3',[1 30*22050],1,2);
/usr/bin/mpg123 -2 -m -n 1150 -q -w /tmp/tmp950.wav "thompson_twins--Into_The_Gap--Hold_Me_Now--3.mp3"
 % Convert to MFCCs very close to those genrated by feacalc -sr 22050 -nyq 8000 -dith -hpf -opf htk -delta 0 -plp no -dom cep -com yes -frq mel -filt tri -win 32 -step 16 -cep 20
 [mm,aspc] = melfcc(d*3.3752, sr, 'maxfreq', 8000, 'numcep', 20, 'nbands', 22, 'fbtype', 'fcmel', 'dcttype', 1, 'usecmp', 1, 'wintime', 0.032, 'hoptime', 0.016, 'preemph', 0, 'dither', 1);
 % .. then convert the cepstra back to audio (same options)
 [im,ispc] = invmelfcc(mm, sr, 'maxfreq', 8000, 'numcep', 20, 'nbands', 22, 'fbtype', 'fcmel', 'dcttype', 1, 'usecmp', 1, 'wintime', 0.032, 'hoptime', 0.016, 'preemph', 0, 'dither', 1);
 % listen to the reconstruction
 % compare the spectrograms
 caxis([-50 30])
 title('original music')
 caxis([-40 40])
 title('noise-excited reconstruction from cepstra')
 % Notice how spectral detail is blurred out e.g. the triangle hits around 6 kHz are broadened to a noise bank from 6-8 kHz.
 % save out the reconstruction
ans =
[example of spectrograms before and after MFCC processing]

Other Resources

The de-facto standard Matlab implementation of MFCCs for Matlab is the one in Malcolm Slaney's Auditory Toolbox. This version has been verified to give (nearly) identical results, but offers flexibility to adapt to different bandwidths, sampling rates, etc.

An alternative Matlab implementation of PLP and RASTA can be found in Fernando Santos Perdigão's Auditory/Cochlea Toolbox.

If you use this code in your research and would like to acknowledge it (and direct others to it), you could use a reference like this:

      Author = {Daniel P. W. Ellis},
      Year = {2005},
      Title = {{PLP} and {RASTA} (and {MFCC}, and inversion) in {M}atlab},
      Url = {http://www.ee.columbia.edu/~dpwe/resources/matlab/rastamat/},
      Note = {online web resource}}



H. Hermansky, "Perceptual linear predictive (PLP) analysis of speech", J. Acoust. Soc. Am., vol. 87, no. 4, pp. 1738-1752, Apr. 1990.
H. Hermansky and N. Morgan, "RASTA processing of speech", IEEE Trans. on Speech and Audio Proc., vol. 2, no. 4, pp. 578-589, Oct. 1994.

Last updated: $Date: 2012/09/03 22:59:36 $

Dan Ellis <dpwe@ee.columbia.edu>