Can anyone show me how to evaluate an integral like this by hand? I believe such integrals have an analytic solution, but I can't figure out how to find them. Mathematica seems unable to help (the Integrate command runs forever) but I believe this can be done by hand. It's a sort of integral commonly found in communications theory. I actually don't think it's supposed to be very hard...(adsbygoogle = window.adsbygoogle || []).push({});

[itex]

\int_{ - \infty }^\infty {\left[ {\frac{1}

{{\sqrt T }}\operatorname{sinc} \left( {\frac{t}

{T}} \right) - \frac{1}

{{2\sqrt T }}\operatorname{sinc} \left( {\frac{{t - T}}

{T}} \right)} \right]^2 dt}

[/itex]

where

[itex]

\operatorname{sinc} \left( t \right) \triangleq \frac{{\sin \left( {\pi t} \right)}}

{{\pi t}}

[/itex]

Obviously I can expand the binomial out, but I'm left with products of sinc's with different arguments, and I don't know how to continue.

- Warren

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# Evaluation of a sinc integral

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