AW: [music-dsp] fractional power DFT

Sampo Syreeni decoy at iki.fi
Tue Feb 5 18:14:33 EST 2002


On Tue, 5 Feb 2002, Thomas Grill wrote:

>> This can obviously be computed rapidly using the DFT. I am not
>> sure what it is good for, though.
>
>What i can say for now is what it is good for ;-) In music two
>properties are of predominant importance: time and frequency. Since the
>DFT transforms one into the other it would be artistically fascinating
>to have something in between.

Unless the result is some truly boring linear combination of the time and
frequency domains. Perhaps this isn't the case, here. See below.

>How does a gradual shift from the time to the frequency domain sound?
>This should be worth investigating.....

Yep. This is the "still..." part.

Also Thomas seems to have a point -- MathWorld, sparse though it is,
states at http://mathworld.wolfram.com/FractionalFourierTransform.html :

"The fractional Fourier transform is generally understood to correspond to
a rotation in time-frequency phase space, where the usual Fourier
transform corresponds to a rotation of 90° (pi/2 radians). A fractional
Fourier transform can be used to detect frequencies which are not integer
multiples of the lowest discrete Fourier transform frequency."

This sort of sounds like it could be *quite* useful in applications like
pitch tracking.

Sampo Syreeni, aka decoy - mailto:decoy at iki.fi, tel:+358-50-5756111
student/math+cs/helsinki university, http://www.iki.fi/~decoy/front
openpgp: 050985C2/025E D175 ABE5 027C 9494 EEB0 E090 8BA9 0509 85C2


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