$.$ The continuous$-$time lowpass filter H$($s$)$ has cut$-$off frequency $$c$.$ This filter is transformed to a

lowpass discrete$-$time filter with cut$-$off wp$1$ by substituting $(1-$z$-1$

$)/(1+$z$-1$

$)$ for s$.$ H$($s$)$ is transformed

to a highpass discrete$-$time filter with cut$-$off wp$2$ by substituting $(1+$z$-1$

$)/(1-$z$-1$

$)$ for s$.$

$($a$)$ Find $$c in terms of wp$1.$

$($b$)$ Find $$c in terms of wp$2.$

$($c$)$ Find a simple relationship between wp$2$ and wp$1$