Problem 3:

2.5 A filter has impulse response h(t) shown in Figure 2.68.

h(t) = -pr(t) + pr(t – T) + pr(t − 2T) - pr(t - 3T)

+ pr(t - 4T) - pr(t – 5T) – pr(t – 6T)

129

Note that each pulse lasts Ţ seconds since the plot has a scale of t/T.

(a) The input x(1) to the filter is a single rectangular pulse of duration T.

Find the output of the filter. Plot this from time-T to time 9T.

(b) Using the result above and superposition (linearity principle), find the output due to the sequence of pulses shown in Figure 2.70.

Plot the output from time - 1 to time 15T./nh(t)

Figure 2.68

Figure 2.68 Impulse response for Problem 2.5.

t/T

Ly