The spectrogram is a standard sound visualization tool, showing the distribution of energy in both time and frequency. It is simply an image formed by the magnitude of the short-time Fourier transform, normally on a log-intensity axis (e.g. dB).
Matlab's Signal Processing Toolbox has a built-in specgram function, but to support students who had not purchased that toolbox, I wrote a drop-in replacement.
The return value of specgram is a complex array that contains enough information to fully reconstruct the original signal. I've written an inverse routine, ispecgram that will recreate sound from a (possibly modified) output of specgram.
For contrast, I've also written a function to plot spectrograms on a log-frequency axis. This isn't a very sophisticated version - it just performs a mapping of the linear-frequency bins from the FFT (rather than, say, varying the time window at different frequencies). But it shows the differences in this kind of display well enough.
I've included a second version of this log-frequency mapping, also known as constant-Q (i.e. the bandwidth-to-center-frequency ration is constant). This version attempts to preserve information enough information in the log-frequency domain to reconstruct the linear-frequency spectrogram with minimal distortion, to allow iterative mapping between the two spectral axes.
The code fragment below makes a simple comparison of linear and log-frequency spectrograms.
The routines provided here are:
An example use is shown below:
>> % Load a speech waveform >> [d,sr] = wavread('sf2_cln.wav'); >> >> % Conventional (linear-frequency) spectrogram >> subplot(311) >> specgram(d,1024,sr); >> % Log-frequency spectrogram >> subplot(312) >> logfsgram(d,1024,sr); >> % Recover approx to lin-F from log-F >> [Y,MX]=logfsgram(d,1024,sr); >> DR = sqrt(MX'*(Y.^2)); >> subplot(313) >> imagesc(20*log10(DR)) >> caxis([-100 30])
Notice how the bottom quarter of the lin-freq specgtrogram is expanded to almost all of the log-freq spectrogram, and how the sets of harmonic partials that are equally-spaced but stretching apart on the left become a pattern of unequally-spaced features moving in parallel on the right. Also notice how mapping the log-resolution spectrogram back to the lin-freq bins (with the MX mapping matrix returned by logfsgram) results in blurring in the higher frequency bins.
Here's an example of using the logfmap matrix:
>> % Start with the basic (linear-freq) spectrogram matxix >> D = log(abs(specgram(d,512))); >> % We're going to do the mapping in the log-magnitude domain >> % so let's shift D so that a value of zero means something. >> minD = min(min(D)); >> D = D - minD; >> subplot(311) >> imagesc(D); axis xy >> c = caxis; >> >> % Design the mapping matrix to lose no bins at the top but 5 at the bottom >> [M,N] = logfmap(257,6,257); >> size(M) ans = 1006 257 >> % Our 257 bin FFT expands to 1006 log-F bins >> % Perform the mapping: >> MD = M*D; >> subplot(312) >> imagesc(MD); axis xy >> caxis(c); >> % Map back to the original axis space, just to check that we can >> NMD = N*MD; >> subplot(313) >> imagesc(NMD); axis xy >> caxis(c) >> % Most bins look the same, except for the band that we lost at the bottom