Saturday, February 05, 2005

FFT Properties

Types of Fourier Transforms
1.Continuous Time Fourier Transform (CTFT), or Fourier Transforms
2.Continuous Time Fourier Series (CTFS), or Fourier Series
3.Discrete Time Fourier Transform (DTFT)
4.Discrete Time Fourier Series (DTFS)
CFS: A periodic function f(t) with period T: f(t) = f(t+T), F[k]= ..., f(t)=...
DFT: A discrete signal, i.e. a sequence f[n], can be described by DFT: F(ejw)=... f[n]=...
DFS: If a discrete time sequence is periodic with period N: f[n] = f[n+Nl], F[k]=... f[n]=...

Especially for Duality
For Discrete Fourier Series:
If x[n]->(dfs) X[k], then
X[n]->(dfs) Nx[-k]
Similar case for DFT

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