Homework: Difference between revisions

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Line 43: Line 43:
\left \langle \phi_k(t) \vert \phi_l(t) \right \rangle
\left \langle \phi_k(t) \vert \phi_l(t) \right \rangle
\end{matrix}
\end{matrix}

</math>
</math>
<br>
By earlier work:
<math>
\left \langle \phi_k(t) \vert \phi_l(t) \right \rangle
=T\delta_{l,k}
</math>
<br>
<math>
\Rightarrow
\sum_{k=-\infty}^{\infty}\sum_{l=-\infty}^{\infty} x(kT)x(lT)
\left \langle \phi_k(t) \vert \phi_l(t) \right \rangle
=T\sum_{k=-\infty}^{\infty} \left | x(kT) \right |^2
</math>
<br>
<math>
\Rightarrow
\sum_{k=-\infty}^{\infty} \left | x(kT) \right | ^2
=1/T\int_{-\infty}^{\infty} \left | x(t) \right | ^2\,dt
</math>
==Homework #13==
Total time spent working on Wiki: 3.5 hrs

Revision as of 09:34, 10 December 2004

Homework #9

Problem Statement:
Show that, for a bandwidth limited signal ( with )

And find c.

Equations:


Solution:



By earlier work:

Homework #13

Total time spent working on Wiki: 3.5 hrs