Description: Program FFT2SURF plots double Fourier series representations for several different surfaces. 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 doubly periodic function with periods px and py has the approximate form: f(x,y) = sum( exp(2i*pi/px*k*x)*c(k,m)*exp(2i*pi/py*m*y),... k=n:n, m=n:n) If the function has discontinuities, a better approximation can sometimes be produced by using a smoothed function fa(x,y) obtained by local averaging of f(x,y) as follows: fa(x,y) = integral(f(x+u,y+v)*du*dv, s<u<+s, s<v<+s )/(4*s^2) where s is a small fraction of min(px,py). Wherever f(x,y) is smooth, f and fa will agree closely, but sharp edges of f(x,y) get rounded off in the averaged function fa(x,y). The Fourier coefficients ca(k,m) for the averaged function are simply ca(k,m) = c(k,m)*sig(k,m) where the sigma factors sig(k,m) are sig(k,m) = sin(sin(2*pi*s*k/px)*sin(2*pi*s*m/py)/... ((2*pi*s*k/px)*(2*pi*s*m/py)) ( SEE Chapter 4 of 'Applied Analysis' by Cornelius Lanczos )
License: Freeware Related: sltvlt, Small, Fraction, minpxpy, sltult, integralfx buy bvdudv, smoothed, obtained, Local, averaging, agree, closely, piskpx pismpy, sinsin piskpxsin pismpy, chapter, applied O/S:BSD, Linux, Solaris, Mac OS X File Size: 10.0 KB Downloads: 6

