A certain wireless channel has the following impulse response: h(t) = k1(t) + k2(t ) (a) Determine the frequency response of the overall system if the transmit and receiver lters are given by G(f) and C(f). (b) Determine the frequency response of the transmit and receive lters if the system is designed to completely mitigate the ISI by using an ideal Nyquist pulse. Assume that the channel is compensated solely at the transmitter. (c) Determine the frequency response of the transmit and receive lters if the system is designed to completely mitigate the ISI by using a raised cosine pulse with a roll-o factor = 0:5. Assume that the channel is compensated equally at the transmitter and receiver. (d) Determine the frequency response of the transmit and receive lters if the system is designed to completely mitigate the ISI by using a full raised cosine pulse. Assume that the channel is only compensated solely at the receiver.

The idea that, for each pair of devices v and w, there’s a strict dichotomy between being “in range” or “out of range” is a simplified abstraction. more accurately, there’s a power decay function f (·) that specifies, for a pair of devices at distance δ, the signal strength f(δ) that they’ll be able to achieve on their wireless connection. (we’ll assume that f (δ) decreases with increasing δ.) we might want to build this into our notion of back-up sets as follows: among the k devices in the back-up set of v, there should be at least one that can be reached with very high signal strength, at least one other that can be reached with moderately high signal strength, and so forth. more concretely, we have values p1 ≥ p2 ≥ . . ≥ pk, so that if the back-up set for v consists of devices at distances d1≤d2≤≤dk,thenweshouldhavef(dj)≥pj foreachj. give an algorithm that determines whether it is possible to choose a back-up set for each device subject to this more detailed condition, still requiring that no device should appear in the back-up set of more than b other devices. again, the algorithm should output the back-up sets themselves, provided they can be found.\