Manual spectrogram creation without using spectrogram command

I have a signal y which I need to create spectrograms of it with these parameters without using the spectrogram command

Time-domain window size: use the following values {16; 64; 256; 1024; 4096} ( meaning to split the signal 5 times, first time into windows of length 16, second into windows of length 64 and so on)

Overlap between the sliding windows: 50% (meaning if the first part is 1:16 the second is 9:24 & the third is 17:32 and so on)

FFT size: 2^13 (meaning to use 2^13 samples of the signal only)

Create a spectrogram for each window size ({16; 64; 256; 1024; 4096}) using a rectangular time-domain window.

What I'm actually stuck at is how to implement the window splitting thing, I thought of using a for loop and after splitting the windows and taking the FFTs creating the spectrogram with imagesc but not really seeing how the splitting and storing the FFT values of each window should go

Answer 1

[Mathieu NOE]

hello

see below (myspecgram)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% load signal
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% data
[data,Fs] = audioread('myWAVaudiofile.wav');

channel = 1;
signal = data(:,channel);
samples = length(signal);

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% FFT parameters
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
NFFT = 4096;    % 
OVERLAP = 0.75;

% spectrogram dB scale
spectrogram_dB_scale = 100;  % dB range scale (means , the lowest displayed level is XX dB below the max level)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% options 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%% decimate (if needed)
% NB : decim = 1 will do nothing (output = input)
decim = 2;
if decim>1
    signal = decimate(signal,decim);
    Fs = Fs/decim;
end


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% display 2 : time / frequency analysis : spectrogram demo
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% [sg,fsg,tsg] = specgram(signal,NFFT,Fs,hanning(NFFT),floor(NFFT*OVERLAP));  
[sg,fsg,tsg] = myspecgram(signal,NFFT,Fs,OVERLAP);  

% FFT normalisation and conversion amplitude from linear to dB (peak)
sg_dBpeak = 20*log10(abs(sg))+20*log10(2/length(fsg));     % NB : X=fft(x.*hanning(N))*4/N; % hanning only

% saturation of the dB range : 
% saturation_dB = 60;  % dB range scale (means , the lowest displayed level is XX dB below the max level)
min_disp_dB = round(max(max(sg_dBpeak))) - spectrogram_dB_scale;
sg_dBpeak(sg_dBpeak<min_disp_dB) = min_disp_dB;

% plots spectrogram
figure(2);
imagesc(tsg,fsg,sg_dBpeak);colormap('jet');
axis('xy');colorbar('vert');grid
title([' Spectrogram / Fs = ' num2str(Fs) ' Hz / Delta f = ' num2str(fsg(2)-fsg(1)) ' Hz ']);
xlabel('Time (s)');ylabel('Frequency (Hz)');




function  [sg,freq_vector,time] = myspecgram(signal,nfft,Fs,Overlap)
% [sg,freq_vector,time] = myspecgram(signal,NFFT,Fs,hanning(NFFT),floor(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)
dt = 1/Fs;
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
    sg = [];
    for i=1:spectnum
        start = (i-1)*offset;
        sw = signal((1+start):(start+nfft)).*window;
        sg = [sg (abs(fft(sw))*4/nfft)];     % X=fft(x.*hanning(N))*4/N; % hanning only 
        time(i) = (start+nfft/2)*dt; % time defined as in the middle of the data buffer
    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
    
sg = sg(select,:);
freq_vector = (select - 1)*Fs/nfft;

end 

[Roozbeh]

It seems that "Decimate" is available only in "Signal_Processing_Toolbox"!

[Mathieu NOE]

@Roozbeh

yes , remove that portion of the code if needed

but it's worth having the Signal Processing Toolbox if you are in that job !