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Fourier series with sigma approximation 1.0
File ID: 84031






Fourier series with sigma approximation 1.0
Download Fourier series with sigma approximation 1.0http://www.mathworks.comReport Error Link
License: Shareware
File Size: 10.0 KB
Downloads: 7
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Fourier series with sigma approximation 1.0 Description
Description: Program FFTSIGMA plots Fourier series representations with sigma approximation. The figures show effects of
the number of series terms and use of Lanczos sigma factors
to smooth Gibbs oscillations. The Fourier series of a periodic function with period px has the approximate
form:

f(x) = sum( exp(2i*pi/px*k*x)*c(k),...
k=-n:n)

If the function has discontinuities, a better approximation
can sometimes be produced by using a smoothed function fa(x)
obtained by local averaging of f(x) as follows:

fa(x) = integral(f(x+u)*du, -s<u<+s )/(2*s)

where s is a small fraction of px. Wherever f(x) is
smooth, f and fa will agree closely, but sharp edges of f(x)
get rounded off in the averaged function fa(x). The Fourier
coefficients ca(k) for the averaged function are simply
ca(k) = c(k)*sig(k) where the sigma factors sig(k) are
sig(k) = sin(sin(2*pi*s*k/px)*/(2*pi*s*k/px))
( SEE Chapter 4 of 'Applied Analysis' by Cornelius Lanczos )

License: Shareware

Related: Dnn, discontinuities, exp ipipxkxck, approximate, Function, period, produced, averaging

O/S:BSD, Linux, Solaris, Mac OS X

File Size: 10.0 KB

Downloads: 7



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The output figures will show effects of the number of series terms and use of the Lanczos sigma factors to smooth the Gibbs oscillations.

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