why does spectrogram of stft shows different magnitude while changing the window size?

fs=5000; % Sampling rate
N=1000; % Number of data points
y=sin(500*pi*[0:1:N-1]/fs)...
    +2*sin(500*1.5*pi*[0:1:N-1]/fs)...
    +3*sin(500*3*pi*[0:1:N-1]/fs)...
    +4*sin(500*4*pi*[0:1:N-1]/fs);t=[0:1:N-1]/fs; 
 
figure(1); 
windowsize = 200; 
window = boxcar(windowsize); 
nfft = windowsize; 
noverlap = windowsize-1; 
[S,F,T] = spectrogram(y,window,noverlap,nfft,fs); 
imagesc(T,F,(abs(S))) 
set(gca,'YDir','Normal') 
xlabel('Time (secs)') 
ylabel('Freq (Hz)') 
title('Short-time Fourier Transform spectrum')

For the above signal, the expected amplitudes of frequencies are in the range 1-4. once we i do the stft with window size 200, i am getting amplitudes of frequency in the range of 0-400 Hz. if i reduce the window size to 16, the amplitudes moving to the range of 0-45 Hz. Did i do anything wrong in my code or am i conceptually wrong somewhere?

Answer 1

[Mathieu NOE]

hello

I was tired of not being able to understand why some matlab functions (mostly based on fft) would not scale the output as I was expecting.

Finally decided (long time ago) to rewritte the spectrogram function myself - now the amplitude of the spectrogram are ok with the input data. I only decided to simplify the function, so it's only hanning window for the time being. If you change the type of window , you have to correct for the new correction coefficient.

also the overlap is a percentage of nfft (most of the time I leave it at 75%)

hope it helps

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