Homework

Homework #9

Problem Statement:
Show that, for a bandwidth limited signal ($x(t)$ with $f_{max}<\frac{1}{2T}$)
$\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}{|x(kT)|}^2=c\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}{|x(t)|}^{2}dt$
And find c.

Equations:
$⟨{\varphi }_k(t)|{\varphi }_l(t)⟩=\underset{-\mathrm{\infty }}{\overset{\mathrm{\infty }}{\int }}{\varphi }_k(t{)}^{*}{\varphi }_l(t)dt$
$x(t)=\sum _{k=-\mathrm{\infty }}^{\mathrm{\infty }}x(kT){\varphi }_k(t)$