The frequency-response characteristic of a low pass channel can be approximated by where W is the…

The frequency-response characteristic of a low pass channel can be approximated by

where W is the channel bandwidth. An input signal s(t) whose spectrum is band-limited to W Hz is passed through the channel.

a. Show that

Thus, the channel produces a pair of echoes.

b. Suppose that the received signal y(t) is passed through a filter matched to s(t). Determine the output of the matched filter at t = kT , k = 0, ±1, ±2, … , where T is the symbol duration.

c. What is the ISI pattern resulting from the channel if t0 = T ?

 

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