Manual implementation of Matlab spectogram function - matlab

Question

I am trying to implement my own function that gives the same results as Matlab spectogram function.
So far I have accomplished function like this:
function out = manulaSpectogram(x, win, noverlap, nfft)
x = x(:);
n = length(x);
wlen = length(win);
nUnique = ceil((1+nfft)/2); % number of uniqure points
L = fix((n-noverlap)/(wlen-noverlap)); % number of signal frames
out = zeros(L, nUnique);
index = 1:wlen;
for i = 0:L-1
xw = win.*x(index);
X = fft(xw, nfft);
out(i+1, :) = X(1:nUnique);
index = index + (wlen - noverlap);
end
end
In my tests it works perfectly and gives the same results like spectogram function when parameter nfft is greater or equal to length of window.
% first test (nnft = window length):
A = [1,2,3,4,5,6];
window = 6;
overlap = 2;
nfft = 6;
s = spectrogram(A, hamming(window), overlap, nfft)'
s2 = manulaSpectogram(A, hamming(window), overlap, nfft)
% results:
s =
9.7300 + 0.0000i -5.2936 + 0.9205i 0.7279 - 0.3737i -0.1186 + 0.0000i
s2 =
9.7300 + 0.0000i -5.2936 - 0.9205i 0.7279 + 0.3737i -0.1186 + 0.0000i
% second test (nfft > window length):
A = [1,2,3,4,5,6];
window = 3;
overlap = 2;
nfft = 6;
s = spectrogram(A, hamming(window), overlap, nfft)'
s2 = manulaSpectogram(A, hamming(window), overlap, nfft)
% results:
s =
2.3200 + 0.0000i 0.9600 + 1.9399i -1.0400 + 1.5242i -1.6800 + 0.0000i
3.4800 + 0.0000i 1.5000 + 2.8752i -1.5000 + 2.3209i -2.5200 + 0.0000i
4.6400 + 0.0000i 2.0400 + 3.8105i -1.9600 + 3.1177i -3.3600 + 0.0000i
5.8000 + 0.0000i 2.5800 + 4.7458i -2.4200 + 3.9144i -4.2000 + 0.0000i
s2 =
2.3200 + 0.0000i 0.9600 - 1.9399i -1.0400 - 1.5242i -1.6800 + 0.0000i
3.4800 + 0.0000i 1.5000 - 2.8752i -1.5000 - 2.3209i -2.5200 + 0.0000i
4.6400 + 0.0000i 2.0400 - 3.8105i -1.9600 - 3.1177i -3.3600 + 0.0000i
5.8000 + 0.0000i 2.5800 - 4.7458i -2.4200 - 3.9144i -4.2000 + 0.0000i
In the case when length of window is less than nfft than the results are different.
% third test (nfft < window length):
A = [1,2,3,4,5,6];
window = 6;
overlap = 2;
nfft = 3;
s = spectrogram(A, hamming(window), overlap, nfft)'
s2 = manulaSpectogram(A, hamming(window), overlap, nfft)
% results:
s =
9.7300 + 0.0000i 0.7279 - 0.3737i
s2 =
3.6121 + 0.0000i -1.6861 + 1.6807i
So how can I improve my function to recieve the same results even in the case when nnft is less than window length? How Matlab's spectogram calculates this case?
I am trying to implement my own function because a spectogram function is a part of a large algorithm which I need to implement from Matlab to C# language so I would like to know what spectogram "black box" does..

Answer 1

I noticed that when window size is greater than nfft scalar number, the data has to be transformed somehow. Finally I found an inner Matlab function that probably is called in the original spectogram Matlab function. It is named datawrap and wraps input data modulo nfft.
So in my function I had to transform data segment (in the same way how datawrap function does it) before calling fft.
Improved function:
function out = manulaSpectogram(x, win, noverlap, nfft)
x = x(:);
n = length(x);
wlen = length(win);
nUnique = ceil((1+nfft)/2); % number of uniqure points
L = fix((n-noverlap)/(wlen-noverlap)); % number of signal frames
out = zeros(L, nUnique);
index = 1:wlen;
for i = 0:L-1
xw = win.*x(index);
% added transformation
if length(xw) > nfft
xw = sum(buffer(xw, nfft), 2);
end
% end of added transformation
X = fft(xw, nfft);
out(i+1, :) = X(1:nUnique);
index = index + (wlen - noverlap);
end
end
I believe it works properly because it gives the same results as Matlab spectogram function.

Answer 2

With the window you are calculating the ends of the block to zero. This needs as mandatory, that the vector lengths of the window and the FFT-Block are the same. Matlab allows with the default parameters unequal values: nsc is not equal to nff (see Matlab docu spectrogram with default). An error message would be necessary if different block length for the window and nff occur. Matlab spectrogram with default parameter for my opinion is wrong. Compare with LabView, Dasylab, Hewlett-Packard and http://www.schmid-werren.ch/hanspeter/publications/2012fftnoise.pdf