Can anyone explain me this code of mel spaced filter banks? i have to use this in my speaker recognition project.

function m = melfb(p, n, fs)

% MELFB Determine matrix for a mel-spaced filterbank %

% Inputs: p number of filters in filterbank

% n length of fft

% fs sample rate in Hz %

% Outputs: x a (sparse) matrix containing the filterbank amplitudes

% size(x) = [p, 1+floor(n/2)] %

f0 = 700 / fs;

fn2 = floor(n/2);

lr = log(1 + 0.5/f0) / (p+1);

% convert to fft bin numbers with 0 for DC term

bl = n * (f0 * (exp([0 1 p p+1] * lr) - 1));

b1 = floor(bl(1)) + 1;

b2 = ceil(bl(2));

b3 = floor(bl(3));

b4 = min(fn2, ceil(bl(4))) - 1;

pf = log(1 + (b1:b4)/n/f0) / lr;

fp = floor(pf);

pm = pf - fp;

r = [fp(b2:b4) 1+fp(1:b3)];

c = [b2:b4 1:b3] + 1;

v = 2 * [1-pm(b2:b4) pm(1:b3)];

m = sparse(r, c, v, p, 1+fn2);

Answer 1

[Hari]

Hi,

I understand that you’re trying to use the melfb function in your speaker recognition project, and you're seeking an explanation of how the code generates mel filter banks from FFT bins.

I assume that you're familiar with basic signal processing and the concept of mel-scale filtering, but need clarity on how the code translates mel-scale logic into filter bank computation using MATLAB.

In order to understand how this code computes mel-spaced triangular filter banks, you can follow the below explanation:

Step 1: Set up mel frequency conversion parameters

The mel scale approximates human hearing and is calculated as:

mel(f) = log(1 + f/700)

The variable f0 = 700/fs and lr = log(1 + 0.5/f0)/(p+1) convert frequency to mel-space and divide the mel scale evenly.

Step 2: Determine filter bank edges in FFT bins

The code computes boundaries for p filters across the spectrum:

• bl = n * (f0 * (exp([...]) - 1)) maps evenly spaced mel points back to linear frequency (in FFT bin numbers).
• b1, b2, b3, and b4 define the valid range of bins contributing to the filter bank.

Step 3: Compute triangular weights for filters

• pf converts bin indices to positions in mel space.
• fp gives the lower bin of the triangle for each frequency.
• pm gives the fractional part for linear interpolation.
• The vectors r, c, and v form the row indices, column indices, and values of the sparse matrix.

Step 4: Construct sparse filter bank matrix

• m = sparse(r, c, v, p, 1+fn2) builds a p × (n/2 + 1) matrix.
• Each row in m is a triangular filter centered at a mel-scaled frequency, used to convert FFT magnitudes to mel-filtered energy.

This matrix m is used to transform the FFT magnitude spectrum into mel filterbank energies, essential in computing MFCCs for speaker recognition.

Refer to the documentation of:

• "sparse": https://www.mathworks.com/help/matlab/ref/sparse.html
• "floor": https://www.mathworks.com/help/matlab/ref/floor.html
• "exp": https://www.mathworks.com/help/matlab/ref/exp.html

Hope this helps!