Fourier series
Introduction
in progress... working on it offline... will upload tonight - Jeff (6pm, 10/6/05)
Periodic Functions
A continuous time signal is said to be periodic if there is a positive nonzero value of T such that
for all
Dirichlet Conditions
The conditions for a periodic function with period 2L to have a convergent Fourier series.
Theorem:
Let be a piecewise regular real-valued function defined on some interval [-L,L], such that has only a finite number of discontinuities and extrema in [-L,L]. Then the Fourier series of this function converges to when is continuous and to the arithmetic mean of the left-handed and right-handed limit of at a point where it is discontinuous.
The Fourier Series
A Fourier series is an expansion of a periodic function in terms of an infinite sum of sines and cosines. Fourier series make use of the orthogonality relationships of the sine and cosine functions.
.
see also:Orthogonal Functions
Principle author of this page: Aric Goe
Introduction added on 10/06/05 by Jeff W