# short time fourier transform

10 views (last 30 days)
Richard on 9 Dec 2012
I would like to perform a short time fourier transform (STFT) to a synthetic data series. I can compute the fourier transform by:
fs = 40;
t = 0:(1 / fs):4;
y1 = [sin(2 * pi * 5 * t(t <= 2)), sin(2 * pi * 10 * t(t > 2))];
subplot(311);
plot(t,y1,'k');
Fy1 = abs(ifft(y1));
N = numel(t);
idx = 1:numel(Fy1) / 2; % # Indices of half the spectrum
f = fs * (0:(N - 1)) / N; % # Actual frequencies
subplot(312);
plot(f(idx),2*Fy1(idx),'k');
As a third subplot, I would now like to compute the STFT otherwise known as the windowed fourier transform, which will show hoe the frequency of the signal varies in time. How can this be done?

Matt J on 9 Dec 2012
##### 2 CommentsShowHide 1 older comment
Matt J on 13 Dec 2012
Once you have the STFT, you can obtain the spectrogram as abs(STFT).^2

Wayne King on 13 Dec 2012
Why not just use spectrogram if you have the Signal Processing Toolbox?
You can output the STFT and/or the short-time periodograms (PSD estimates)
##### 1 CommentShowHide None
Richard on 13 Dec 2012
I have tried using the spectrogram. By typing spectrogram(y1), matlab returns a plot, but I cannot get the spectrogram to display the results in a format that follows from subplot(311) and (312) above. For example, I would like the time along the x axis and the frequency along the y.

Wayne King on 13 Dec 2012
Then just use the 'yaxis' option
t = 0:0.001:1-0.001;
x=chirp(t,0,1,150);
spectrogram(x,'yaxis')
If you actually output arguments from spectrogram, you have much more control over the plot. See the help.