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# Manual implementation of spectogram function

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Pawel Krzyzak on 29 Apr 2021
Edited: Pawel Krzyzak on 29 Apr 2021
Hello,
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?
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### Accepted Answer

Pawel Krzyzak on 29 Apr 2021
Edited: Pawel Krzyzak on 29 Apr 2021
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.
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### More Answers (1)

Mathieu NOE on 29 Apr 2021
hello
I share with you my own version , hope it helps !
notice i always use hanning window and the correction factor for amplitude is related to this choice
fs=5000; % Sampling rate
N=1000; % Number of data points
t=[0:1:N-1]/fs;
y=sin(500*pi*t)...
+2*sin(500*1.5*pi*t)...
+3*sin(500*3*pi*t)...
+4*sin(500*4*pi*t);
figure(1);
windowsize = 200;
window = boxcar(windowsize);
nfft = windowsize;
noverlap = windowsize-1;
% [S,F,T] = spectrogram(y,window,noverlap,nfft,fs); % S = SPECTROGRAM(X,WINDOW,NOVERLAP,NFFT,Fs)
[S,F,T] = myspecgram(y, fs, nfft, 0.75); % overlap is 75% of nfft here
imagesc(T,F,(abs(S)))
colorbar('vert');
set(gca,'YDir','Normal')
xlabel('Time (secs)')
ylabel('Freq (Hz)')
title('Short-time Fourier Transform spectrum')
colormap('jet');
function [fft_specgram,freq_vector,time] = myspecgram(signal, Fs, nfft, Overlap)
% FFT peak spectrogram of signal (example sinus amplitude 1 = 0 dB after fft).
% signal - input signal,
% Fs - Sampling frequency (Hz).
% nfft - FFT window size
% Overlap - buffer overlap % (between 0 and 0.95)
signal = signal(:);
samples = length(signal);
% fill signal with zeros if its length is lower than nfft
if samples<nfft
s_tmp = zeros(nfft,1);
s_tmp((1:samples),:) = signal;
signal = s_tmp;
samples = nfft;
end
% window : hanning
window = hanning(nfft);
window = window(:);
% compute fft with overlap
offset = fix((1-Overlap)*nfft);
spectnum = 1+ fix((samples-nfft)/offset); % Number of windows
% % for info is equivalent to :
% noverlap = Overlap*nfft;
% spectnum = fix((samples-noverlap)/(nfft-noverlap)); % Number of windows
% main loop
fft_specgram = [];
for ci=1:spectnum
start = (ci-1)*offset;
sw = signal((1+start):(start+nfft)).*window;
fft_specgram = [fft_specgram abs(fft(sw))*4/nfft]; % X=fft(x.*hanning(N))*4/N; % hanning only
end
% one sidded fft spectrum % Select first half
if rem(nfft,2) % nfft odd
select = (1:(nfft+1)/2)';
else
select = (1:nfft/2+1)';
end
fft_specgram = fft_specgram(select,:);
freq_vector = (select - 1)*Fs/nfft;
% time vector
% time stamps are defined in the middle of the buffer
time = ((0:spectnum-1)*offset + round(offset/2))/Fs;
end
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Pawel Krzyzak on 29 Apr 2021
Thank your very much for your implementation but I still don't know how can I modify my function to recieve the same results as results given by matlab spectogram funcion.

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