Fourier series with sigma approximation
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 )
Cite As
Abhishek Ballaney (2024). Fourier series with sigma approximation (https://www.mathworks.com/matlabcentral/fileexchange/29720-fourier-series-with-sigma-approximation), MATLAB Central File Exchange. Retrieved .
MATLAB Release Compatibility
Platform Compatibility
Windows macOS LinuxCategories
Tags
Acknowledgements
Inspired by: Double Fourier Series Surface Plotting
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!Discover Live Editor
Create scripts with code, output, and formatted text in a single executable document.
Version | Published | Release Notes | |
---|---|---|---|
1.0.0.0 |