Solve the following problem:
A pulse and its (raised cosine) spectral characteristic are shown in Figure . This pulse is used for transmitting digital information over a band-limited channel at a rate 1/T symbols/s.
a. What is the roll-off factor β?
b. What is the pulse rate?
c. The channel distorts the signal pulses. Suppose the sampled values of the filtered received pulse x(t) are as shown in Figure c. It is obvious that there are five interfering signal components. Give the sequence of +1s and -1s that will cause the largest (destructive or constructive) interference and the corresponding value of the interference (the peak distortion).
d. What is the probability of occurrence of the worst sequence obtained in (c), assuming that all binary digits are equally probable and independent?
