How is Spectrogram function working?

Hello Matlab Community,

I am trying to understand the script of Spectrogram function which takes the short time fourier transform of a signal. IS is doing the same thing as I shown below? We can also divide the x into n segments.

For a x signal.

fftx= fft(x);
gxx= abs(fftx).^2;  % doubles sided spectral density
sxx= 2*gxx(2:length(gxx)/2,:); % calculating single sided spectra 
sxx= [gxx(1,:);sxx;gxx(length(gxx)/2+1,:)]; % Concatenate to get final vector

Answer 1

[Mathieu NOE]

see my demo code below , which replicates the principle of spectrogram

• split the signal (with overlap)
• apply window
• fft
• average

[signal, Fs] = audioread ("test_voice_mono.wav");
 
nfft = 1024; % fft / frame length
overlap = 0.5; % window overlap % overlap is 50% of nfft here

[S,F,T] = myspecgram(signal, Fs, nfft, overlap); 


figure(1); 
imagesc(T,F,20*log10(abs(S))) 
colorbar('vert');
set(gca,'YDir','Normal') 
xlabel('Time (secs)') 
ylabel('Freq (Hz)') 
title('Short-time Fourier Transform spectrum (dB Scale)')
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(nfft/2))/Fs;

end