MCEP Alpha Calculator

Mel-Cepstral analysis of speech data, such as with the help of the SPTK toolkit, requires specifying an all-pass constant (alpha) that determines how the frequency axis is warped. This constant depends on the sampling frequency of the speech data at hand.

This project provides a tool that allows you to calculate the appropriate alpha paramater for a given sampling frequency.


This project is written in Go ( Having installed the "go" compilation tools, please run

$ go build

in this directory to build.

You could also download precompiled binaries from the "Downloads" page on Bitbucket.


$ ./mcep_alpha_calc -f 16000

Technical Details

The Mel-Scale is estimated using the formula noted in Fant (1968)

m = (1000/log(2)) * log(1 + f/1000)

This curve is estimated at equally spaced points between [0,samp_freq/2] and normalized. Given an alpha value, the phase response of an all-pass filter is calculated for each of these points using the equation:

~w = arctan{frac{(1-alpha^2) sin(omega)}{(1+alpha^2) cos(omega) - 2alpha}}

We brute-force over different values of alpha between 0 and 1, and find the alpha where the root-mean-squared distance between the warped frequency and the mel scale is minimum.

Sample Output

Generated Alpha for commonly used Frequencies
Frequency Alpha
8000 Hz 0.312
11025 Hz 0.357
16000 Hz 0.410
22050 Hz 0.455
32000 Hz 0.504
44100 Hz 0.544
48000 Hz 0.554