# Difference between revisions of "Homework"

From Class Wiki

(→Homework #9) |
(→Homework #9) |
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\left \langle \phi_k(t) \vert \phi_l(t) \right \rangle |
\left \langle \phi_k(t) \vert \phi_l(t) \right \rangle |
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\end{matrix} |
\end{matrix} |
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− | |||

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