Register to reply

Fourier Series Interval Points

by zorro
Tags: fourier, interval, points, series
Share this thread:
zorro
#1
Nov24-12, 03:14 PM
P: 1,394
Why is Fourier sine series of any function satisfying Dirichlet's theorem, not defined on the discontinuous points whereas we define it for Fourier cosine series?

ex - sine series of f(x) = cosx, 0<=x<=∏ is defined on 0<x<∏

whereas cosine series of f(x) = sinx, 0<=x<=∏ is defined on 0<=x<=∏
Phys.Org News Partner Science news on Phys.org
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
LCKurtz
#2
Nov27-12, 05:39 PM
HW Helper
Thanks
PF Gold
LCKurtz's Avatar
P: 7,663
Quote Quote by Abdul Quadeer View Post
Why is Fourier sine series of any function satisfying Dirichlet's theorem, not defined on the discontinuous points whereas we define it for Fourier cosine series?

ex - sine series of f(x) = cosx, 0<=x<=∏ is defined on 0<x<∏

whereas cosine series of f(x) = sinx, 0<=x<=∏ is defined on 0<=x<=∏
Not sure what you are getting at. The half range Fourier series you mention both converge for all x. In the first case the FS converges to the average of the right and left hand limits at x = 0 of the odd extension of cos(x). In the second case the FS converges to sin(0) = 0 at x = 0. That is because the even extension of sin(x) is continuous at x=0 while the odd extension of cos(x) is not continuous at x = 0.


Register to reply

Related Discussions
Fourier series of functions with points of discontinuity Topology and Analysis 9
Fourier series on a general interval [a, a + T] Topology and Analysis 5
Fourier Coefficients for asymmetric interval Calculus & Beyond Homework 2
Need help to find application of the Fourier series and Fourier Transforms! Introductory Physics Homework 8
Complex Fourier Series & Full Fourier Series Calculus & Beyond Homework 5