Share
Explore BrainMass

Integrals : Rayleigh's Energy Theorem (Parseval's Theorem)

Evaluate the following integrals using Rayleigh's energy theorem (This is Parseval's theorem for Fourier transforms). All integrals spans between -∞ and ∞.

I1 = ∫ df / [α2 + (2πf)2]

I2 = ∫ sinc2(τf) df

I3 = ∫ df / [α2 + (2πf)2]2

I4 = ∫ sinc4(τf) df

I have added another document with a definition of Rayleigh's theorem and how to use it in a problem.

Please see the attached file for the fully formatted problems.

Attachments

Solution Preview

The explanations are written in the attached Word file.

=======
Here is the plain text:

Evaluate the following integrals using Rayleigh's energy theorem (This is Parseval's theorem for Fourier transforms). All integrals spans between -∞ and ∞.

I1 = ∫ df / [α2 + (2πf)2]

I2 = ∫ sinc2(τf) df

I3 = ∫ df / [α2 + (2πf)2]2

I4 = ∫ sinc4(τf) df

You most likely have tables of Fourier pairs ...

Solution Summary

Rayleigh's energy theorem is applied to evaluating integrals. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

$2.19