FFT

[Magnus Danielson]

From: "Paul Maddox" <Paul.Maddox at unilever.com>
Subject: FFT
Date: Thu, 21 Oct 1999 15:24:29 +0100 (British Summer Time)

> dear all,
> 
>   I know we've touched on this before but... does anyone have
> or know of, a formula for doing a FFT with two waveforms?
> 
>   It seems the waveterm/ppg/wave breakdown the eprom stored
> wave and perform a FFT transform of some kind to get the 
> waves inbetween the two ROM waves...

I don't really understand what you are trying to do here. FFT is a optimized
version of the DFT (Discrete time Fourier Transform). The DFT (and thus FFT)
as well as its inverse form IDFT (and thus IFFT) are linear transforms. This
means that the superposition principle holds on both sides of the transform.

Here are some algebraic rules that may be used.

x = IDFT(DFT(x))

x + y = IDFT(DFT(x) + DFT(y))

a * x = IDFT(a * DFT(x))

x = IDFT(DFT(x)) <=> DFT(x) = DFT(x)

z = x + y <=> DFT(z) = DFT(x) + DFT(y)

a * x = IDFT(a * DFT(x)) <=> DFT(a * x) = a * DFT(x)

a * x + b * y = IDFT(a * DFT(x) + b * DFT(y))

Cheers,
Magnus