mathman
Oct12-04, 10:50 AM
Mathematically, these are three distinct, although related beasts.
Laplace transform (function f(x) defined from 0 to inf) integral of f(x)e-xt, defined for t>=0.
Fourier transform (function f(x) defined from -inf to inf) integral of f(x)e-itx defined for all real t.
Complex Fourier series (function f(x) defined on finite interval - simplify by making it (0,1)) Coeficients (cn) are given by integral of f(x)e-2(pi)inx, where n ranges over all integers. The series terms are cne2(pi)nx
Real Fourier series use sin and cos instead of exp function.
Laplace transform (function f(x) defined from 0 to inf) integral of f(x)e-xt, defined for t>=0.
Fourier transform (function f(x) defined from -inf to inf) integral of f(x)e-itx defined for all real t.
Complex Fourier series (function f(x) defined on finite interval - simplify by making it (0,1)) Coeficients (cn) are given by integral of f(x)e-2(pi)inx, where n ranges over all integers. The series terms are cne2(pi)nx
Real Fourier series use sin and cos instead of exp function.