Re: FFT result evaluation
From: Richard Mathar (mathar_at_amer.strw.leidenuniv.nl)
Date: 11/12/04
- Previous message: Greg Kuperberg: "This week in the mathematics arXiv (1 Nov - 5 Nov)"
- In reply to: Alexander Rentschler: "FFT result evaluation"
- Messages sorted by: [ date ] [ thread ]
Date: Fri, 12 Nov 2004 20:12:42 +0000 (UTC)
In article <cmsmtc$lv2$1@lnx107.hrz.tu-darmstadt.de>,
"Alexander Rentschler" <arentschler@ew.tu-darmstadt.de> writes:
>I have a signal with harmonics that are not integer multiples of the
>fundamental frequency. So it is not possible to guarantee that the FFT -
>Window get a full period of each harmonic of the analysed signal. The result
>of the FFT is a distributed spectrum for each harmonic and it is not
>possible to find out the correct magnitude of the harmonics. Is it possible
>to calculate the correct signal magnitude from the distributed spectrum for
>each harmonic ? I found a way to calculate the magnitude for each
>distributed spectrum, but I don't find the correct mathematical description
>for this problem. Has anybody an idea how to define this mathematically.
>
The FFT (or any other DFT) is covering a finite
range in the time domain and equivalent to multiplication
of the time series by a "boxcar" function. The standard
convolution theorem of Fourier analysis describes
this in the frequency domain as a convolution with
the DFT of the boxcar, known as the sinc-function.
To avoid that the convolution with the "negative" pieces
of the oscillatory sinc-funcion in the frequency domain
"removes" or partially "cancels" the area under the
"correct" peak in the frequency domain, one usually
modifies the boxcar function to "round up" the "sharp"
edges in the time domain and avoid the Gibb's osciallations
of the sinc-function; the keywords to search for
these techniques are "apodisation", "Norton-Beer" ...
This way one can to a good extend ensure that the
area under the "dispersed" peaks in the frequency
domain represents the original's series amplitudes.
http://www.strw.leidenuniv.nl/~mathar
- Previous message: Greg Kuperberg: "This week in the mathematics arXiv (1 Nov - 5 Nov)"
- In reply to: Alexander Rentschler: "FFT result evaluation"
- Messages sorted by: [ date ] [ thread ]
Relevant Pages
|
