$2.$ A delta modulator has the message signal

m$($t$)=40$sin$2$$10$t

a$.$ Determine the minimum sampling frequency required to prevent slope overload,

assuming that the impulse weights $0$ are $.$

b$.$ Does the m$$nimum sampling rate required in the problem a$.$ satisfy the Nyquist

rate? Justify. $($No credit without justification$)$

$3.$ Pulse Code Modulation $($PCM$)$

A continuous data signal is quantized and transmitted using PCM system. If each data

sample at the receiving end of the system must be known to within $0\mathrm{.}125\%$ of the

peak$-$to$-$peak full scale value.

a$.$ How many binary symbols must each transmitted digital word contain?

b$.$ Assume that the message signal is speech for telephone, which has a bandwidth of

$4$ KHz$.$ What is the minimum sampling rate per second without aliasing effect for

this PCM system?