On Sun, Mar 09, 2014 at 12:35:34AM +0200, 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.

There are just two, the FT and the DFT. The only difference between
the last three forms you mention is only a matter of interpretation.

Usually a discrete spectrum is interpreted as the exact spectrum of
a periodic waveform. But it's equally valid to say its the sampled
spectrum of a finite time signal.

A discrete representation in the time domain (i.e. samples) is usually
interpreted as a finite-bandwidth signal (which is the dual of the
second interpretation above), but it's equally valid to say it's the
exact representation of a signal that is periodic in the frequency
domain (the dual of the first interpretation above).

Ciao,

-- 
FA

A world of exhaustive, reliable metadata would be an utopia.
It's also a pipe-dream, founded on self-delusion, nerd hubris
and hysterically inflated market opportunities. (Cory Doctorow)

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