Comments on: HOWTO: From magnitude spectrum to sound http://atlhack.org/2005/10/09/howto-from-magnitude-spectrum-to-sound/ Just another WordPress weblog Wed, 03 Mar 2010 05:26:38 -0500 http://wordpress.org/?v=2.8.4 hourly 1 By: Anonymous http://atlhack.org/2005/10/09/howto-from-magnitude-spectrum-to-sound/comment-page-1/#comment-514 Anonymous Wed, 31 Dec 1969 19:00:00 +0000 #comment-514 Properly, no. The magnitude spectrum throws out the phase information from the DFT transform (what the FFT computes). Given the full DFT, one can exactly reproduce the bandlimited time domain signal - but the phase is critical to positioning the component sinusoids. A short example: <code>load handel; yfft=fft(y); plot( abs( yfft )); %show the spectrum %compare the reconstruction and the original iy=(ifft(yfft)); plot( y ); plot( iy ); iay=ifft(abs(yfft)); plot(iay); sound(iay, Fs);</code> This isn't the best explanation. But the low frequencies of a non-stationary signal are actually doing some weird form of making events in the sound. If you want to throw out the phases of the spectrum but still use the magnitude for synthesis, it might work in the context of short-time fourier transform, where you break the time domain signal into windows (with more or less stationary spectrums) to analyse them. Properly, no. The magnitude spectrum throws out the phase information from the DFT transform (what the FFT computes). Given the full DFT, one can exactly reproduce the bandlimited time domain signal – but the phase is critical to positioning the component sinusoids.

A short example:
load handel;
yfft=fft(y);
plot( abs( yfft )); %show the spectrum

%compare the reconstruction and the original
iy=(ifft(yfft));
plot( y );
plot( iy );

iay=ifft(abs(yfft));
plot(iay);
sound(iay, Fs);

This isn’t the best explanation. But the low frequencies of a non-stationary signal are actually doing some weird form of making events in the sound.

If you want to throw out the phases of the spectrum but still use the magnitude for synthesis, it might work in the context of short-time fourier transform, where you break the time domain signal into windows (with more or less stationary spectrums) to analyse them.

]]> By: Stephen http://atlhack.org/2005/10/09/howto-from-magnitude-spectrum-to-sound/comment-page-1/#comment-515 Stephen Wed, 31 Dec 1969 19:00:00 +0000 #comment-515 I suspected as much. I will go ahead with experimenting with the STFT using just real parts or maybe the magnitudes. This will be my absentee hackfest project for the week. The goal is to create a tool that will convert sounds to images of spectrograms and backwards. Joel mentioned applying applying photoshop filters to them and wondering what the sounds would be. I, of course, am interested in the results of texture synthesis / image analogies on the spectrogram. I suspected as much. I will go ahead with experimenting with the STFT using just real parts or maybe the magnitudes. This will be my absentee hackfest project for the week.

The goal is to create a tool that will convert sounds to images of spectrograms and backwards. Joel mentioned applying applying photoshop filters to them and wondering what the sounds would be. I, of course, am interested in the results of texture synthesis / image analogies on the spectrogram.

]]> By: ynniv http://atlhack.org/2005/10/09/howto-from-magnitude-spectrum-to-sound/comment-page-1/#comment-516 ynniv Wed, 31 Dec 1969 19:00:00 +0000 #comment-516 <a href="http://www.bastwood.com/aphex.php">This website</a> (http://www.bastwood.com/aphex.php) has images hidden in the spectrogram of some Aphex Twin songs. This website (http://www.bastwood.com/aphex.php) has images hidden in the spectrogram of some Aphex Twin songs.

]]> By: Stephen http://atlhack.org/2005/10/09/howto-from-magnitude-spectrum-to-sound/comment-page-1/#comment-525 Stephen Wed, 31 Dec 1969 19:00:00 +0000 #comment-525 The process distorts even sine waves using teensy weensy windows.  Check out the results here:<br /><br /><a href="http://www.cs.ubc.ca/~sfingram/phouriershop/">http://www.cs.ubc.ca/~sfingram/phouriershop/</a><br /><br />I think I'm going to just roll my own photoshop-style filters to run on images with complex pixel values.  Most image filters are quite simple and I think there's nothing wrong with substituting complex numbers in them. The process distorts even sine waves using teensy weensy windows.  Check out the results here:

http://www.cs.ubc.ca/~sfingram/phouriershop/

I think I’m going to just roll my own photoshop-style filters to run on images with complex pixel values.  Most image filters are quite simple and I think there’s nothing wrong with substituting complex numbers in them.

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