# Overview

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# 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.

## Installation

This project is written in Go (www.golang.org). 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.

## Usage

$ ./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

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 |