The raised cosine pulse p(t) is used for zero ISI in digital communications. The expression for p(t) with unity roll-off factor is given by $$$p(t) = {{\sin \,4\,\pi \,W\,t} \over \matrix{ 4\,\pi \,W\,t(1 - 16{W^2}{t^2}) \hfill \cr \hfill \cr \hfill \cr} }$$$ The value of p(t) at $$t = {1 \over {4\,W}}$$ is

In a Direct sequence CDMA system the chip rate is $$1.2288\,\, \times \,\,{10^6}$$ chips per second. If the processing gain is desired to be at least 100. The data rate

The minimum step-size required for a Delta-Modulator operating at 32 K samples/sec to track the signal (here u(t) is the unit-step function)

x(t) = 125t(u(t) - u (t - 1) + (250 - 125t) (u (t - 1) - u (t - 2 )) so that slope - overload is avoided, would be

Choose the correct one from among the alternatives A, B, C, D after matching an item from Group 1 with the most appropriate item in Group 2.

Group
1. FM
2. DM
3. PSK
4. PCM

Group 2
P: Slope overload
Q: $${\mu - law}$$
R: Envelope detector
S: Capture effect
T: Hilbert transform
U: Matched filter