[PD] fft beginner question
matju at artengine.ca
Fri Nov 23 05:56:25 CET 2007
On Wed, 21 Nov 2007, Kyle Klipowicz wrote:
> Even more interesting to me is when my physicist friend told me that
> the Uncertainty Principle is deeply rooted in the trade off between
> time window size and frequency resolution of the FFT. Kinda
> demystifies a whole decade of my life...
That's quite true. It's not about FFT in particular, it's about all of
Fourier methods, and even several other signal decomposition methods than
Fourier. It's about how you can only begin to know a wave by sampling it
at least twice, and the lower the frequency you are trying to extract from
it, the longer the delay between the two samples has to be.
Heisenberg's uncertainty principle is not specific to Quantum Theory, it's
central to the sampling of all wave-like phenomena and more.
If you modify FFT somewhat, you can blow up blocks into little pieces, in
which each frequency is updated exactly as fast as the uncertainty
principle allows it, but I have the impression that it's quite more
complicated to handle, so I never really looked into it.
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