Suppose I create a pulse modulation scheme that I call “Pulse Number Modulation” (PNM). In this PNM scheme, I take every sampling interval, and divide it into K equal sub-intervals. When I transmit pulse data, I transmit either 0, 1, 2, 3, … K pulses in all possible sub-intervals.

For example, if K = 3, then I can transmit a) 0 pulses OR b) 1 pulse in sub-interval 1, OR c) 1 pulse in sub-interval 2, OR d) 1 pulse in sub-interval 3, OR e) 2 pulses in sub-intervals 1 and 2, OR f) 2 pulses in sub-intervals 1 and 3, OR g) 2 pulses in sub-intervals 2 and 3 OR h) 3 pulses in sub-intervals 1, 2 and 3.

A) How many ways can I transmit exactly p pulses among K sub-intervals? Assume p ≤≤ K

B) How many total ways can I transmit pulses in any sampling interval, assuming that the sampling interval is divided into K sub-intervals?

C) We studied 5 pulse modulation schemes in class — PAM, PWM, PCM, PPM and PFM. Which of these schemes is PNM most closely related to?