Homework

Homework #9

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

Equations:
$\left\langle \phi _{k}(t)\vert \phi _{l}(t)\right\rangle =\int _{-\infty }^{\infty }\phi _{k}(t)^{*}\phi _{l}(t)\,dt$
$x(t)=\sum _{k=-\infty }^{\infty }x(kT)\phi _{k}(t)$