On 08/03/2014 22:35, Sampo Syreeni wrote:
There are four basic forms of the theory used in signal processing,
which are all connected but also subtly different. The Fourier transform
is continuous time and continuous frequency. The Fourier series is
periodic time and discrete frequency. The discrete time Fourier
transform is discrete time and periodic frequency. And finally the
discrete Fourier transform is both discrete and periodic in both
frequency and in time.
It took me *ages* to get that shit right, and all that goes on between
them. I was pretty happy then. Then along came you guys, with your
spherical surface harmonics and Fourier-Bessel decompositions. Even the
cylindrical variety. A math friend of mine pointed out number
theoretical transforms and how this all ties in with locally compact
Abelian groups. Abstract harmonical analysis. Then even my engineer pals
suddenly went crazy with discrete cosine transforms, MDCT, modulated and
lapped transforms, time-frequency decompositions, general partitions of
unity, overcomplete bases, L^1 norms, projection pursuits...
An observation - none of this stuff will actually be cool until it
figures in a script for The Big Bang Theory...
Richard Dobson
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