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Re: What are the errors in the FFT? [message #52457 is a reply to message #52441]

Thu, 08 February 2007 10:43

Paul Van Delst[1]
Messages: 1157
Registered: April 2002

Senior Member

monty@lanl.gov wrote:
> For a given function f(t) I am finding:
>
> FFT(FFT(f(t),-1),1) -f(t) varies between about 10^-7 to 1-^-8 for
> floating point
> and about 10^-14 to 10^-16 for double precision

What are the magnitudes of the original f(t)? If close to one, sounds like "simple"
accumulation of precision errors.

> (I.e. the inverse transform of the transform deviates from the
> original function)

Depends on your definition of "deviates".

> Is this aproblem with the IDL implementation of the FFT, or is this a
> more fundamental issue with the algorithm itself?

Depending on your input function magnitudes, it's more likely a (the? :o) fundamental
issue with floating point arithmetic. There are ways of minimising this sort of error
accumulation (and I assume FFT algorithms do it already), but you can't remove it entirely.

cheers,

paulv

--
Paul van Delst Ride lots.
CIMSS @ NOAA/NCEP/EMC Eddy Merckx

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[Message index]

		Re: What are the errors in the FFT? By: Kenneth Bowman on Thu, 08 February 2007 10:24
		Re: What are the errors in the FFT? By: Paul Van Delst[1] on Thu, 08 February 2007 10:45
		Re: What are the errors in the FFT? By: Paul Van Delst[1] on Thu, 08 February 2007 10:43
		Re: What are the errors in the FFT? By: Haje Korth on Thu, 08 February 2007 10:37
		Re: What are the errors in the FFT? By: Vince Hradil on Thu, 08 February 2007 09:38

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