Re: is FFT always approximate?


Michael skrev:
If I have a time signal which is periodic, and I use FFT to obtain the
spectrum, which should be discrete, will this FFT procedure be approximate?

The Fast Fourier Transform, FFT, is an EXACT but efficient
implementation of the Discrete Fourier Transform, DFT. The DFT
is itself an exact representation of a signal discrete-time signal
of finite length.

I am wondering about this because I've heard that FFT is only an
approximation to the true Fourier transform...

The depends on how you define the "true Fourier transform."

There are four different flavours of Fourier transforms. Signals can
be contionuous (C) in time or discrete (D), and they may be of
finite (F) or infinite (I) extend. The four flavours are CI, CF, DI
and DF.

The DFT is exact for the DF case, that is used in digital computers
for practical reasons. If your "real" objective is to analyze one
of the other variations, the DFT must be regarded as an
approximation of what you really want.

Rune

.

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