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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 -&#8734; and &#8734;.

I1 = &#8747; df / [&#945;2 + (2&#960;f)2]

I2 = &#8747; sinc2(&#964;f) df

I3 = &#8747; df / [&#945;2 + (2&#960;f)2]2

I4 = &#8747; sinc4(&#964;f) df

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

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Evaluate the following integrals using Rayleigh's energy theorem (This is Parseval's theorem for Fourier transforms). All integrals spans between -&#8734; and &#8734;.

I1 = &#8747; df / [&#945;2 + (2&#960;f)2]

I2 = &#8747; sinc2(&#964;f) df

I3 = &#8747; df / [&#945;2 + (2&#960;f)2]2

I4 = &#8747; sinc4(&#964;f) 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.

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