$7\mathrm{.}5.$ Let x$($t$)$ be a signal with Nyquist rate $\backslash$omega $\_(0).$ Also, let

y$($t$)=$x$($t$)$p$($t$-1)$

Chap. $7$ Problems

where

p$($t$)=\backslash$sum$\_($n$=-\backslash$infty $)^(\backslash$infty $)\backslash$delta $($t$-$nT$),$ and T$<mi>(</mi><mn>2</mn><mi>\backslash </mi>$pi $)/(\backslash$omega $\_(0)).$

Specify the constraints on the magnitude and phase of the frequency response of a

filter that gives x$($t$)$ as its output when y$($t$)$ is the input.