How can I plot the spectrogram of a sound file without using predefined functions?

Question

How can I plot the spectrogram of a WAV file without using predefined function? i mean i dont want use FFT or spectrogram functions .

my windows i want to take over the whole signal should be Hamming windows with size 256 and overlap 50%.

could you please give me some advice ?

best regards .

i tried the following code for DFT . but i got error : ??? Error using ==> times Matrix dimensions must agree.

the code :

 n=256;
 wholeFile=wavread('C:\Users\alireza\Desktop\alireza bahrami\New folder\Sound clip     32.wav');

for ii = 1:4096
waveform = wholeFile(128*ii + (1:256)); % a bit of background noise...

alpha = 0.54; beta = 1 - alpha; % hamming coefficients
hwin = alpha - beta * cos(2 * pi * (1:n) / (n - 1)); % from http://en.wikipedia.org    /wiki/Window_function#Hamming_window
fSample = 8192; % sampling frequency

t = (0.5:1:n) / fSample; % actual time


waveformHW = waveform .* hwin; % the windowed form of the waveform

frequencies = (0:(n/2)-1) * fSample / n;
myFFT = zeros(size(frequencies));
for fi = 1:n/2
c = cos(2*pi*frequencies(fi) * t);
s = sin(2*pi*frequencies(fi) * t);
myFFT(fi) = (sum(c .* waveformHW) + 1i * sum(s .* waveformHW))/sum(c.*c.*hwin);
end
end
figure; semilogy(frequencies, abs(myFFT))
xlim([0 1000])
xlabel 'frequency'
ylabel 'amplitude'
title 'two tones plus noise'

Answer 1

For my example to work, your t vector must be a column vector, change this line

t = (0.5:1:n) / fSample; % actual time

to

t = (0.5:1:n)' / fSample; % actual time

You can use regress to get the amplitude of the sine and cosine components. Delete this line of your code:

myFFT(fi) = (sum(c .* waveformHW) + 1i * sum(s .* waveformHW))/sum(c.*c.*hwin);

Replace it with

b = regress(waveformHW, [c, s]; % c and s must be column vectors
myFFT(fi) = b(1) + 1i * b(2);