Explore BrainMass

Fourier Analysis and Series : Periodic Functions and Convolution

This content was STOLEN from BrainMass.com - View the original, and get the already-completed solution here!

Please see the attached file for the fully formatted problems.

© BrainMass Inc. brainmass.com October 24, 2018, 10:23 pm ad1c9bdddf


Solution Preview

Please see the attachment.

My book says that you should be able to use f(x) = 1/2(x-t) in problem 2. Then f ~ 1/2 sum from negative infinity to positive ...

Solution Summary

Periodic functions and convolution are investigated. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

See Also This Related BrainMass Solution

Periodic Functions via Convolution

Please see the attached file for the fully formatted problems.

"Periodic Function via Convolution"
Consider the periodic train of Dirac delta "functions"
f(x) =....
with real period ....
(a) FIND and DESCRIBE its Fourier transform F(k). What happens to F if c gets doubled?
(b) Let p(x + c) = p(x) be a periodic function.
Prove or disprove: p(x) is the convolution (i.e. f * g (x) E f(x ? t)g(t) dt) of a periodic train of Dirac delta functions with a non-periodic function, say g(x) in L2 (?co, oo). What is g(x)?
(c) Find the Fourier transform
5(k) FpJ(k) = * f ep(x) dx
of p(x) in terms of the Fourier transform (k) of that nonperiodic function. Relate your answer to the Fourier series coefficients of the periodic function p(x)

View Full Posting Details