$3.(20$pt$)$ A voice signal in the range $20$ Hz to $20$ kHz is sampled at $44100$ samples$=$s$.$ We may

transmit these samples directly as PAM pulses or we may rst convert each sample to a PCM

format and use $($PCM$)$ waveforms for transmission.

$($a$)$ What is the minimum system bandwidth required for the detection of PAM with no ISI

and with a lter roll$-$o characteristic of r $=0$:$5?$

$($b$)$ Using the same lter roll$-$o characteristics, what is the minimum bandwidth required

for the detection of binary $($PCM$)$ waveforms if the samples are quantized to $256$ levels?