Problem 1:

2.3 A data signal consists of an infinite sequence of rectangular pulses of duration T. That is,

s(t) = Σbipr(t-IT),

|=-00

where pr(t) is 1 for 0 ≤ t ≤ T and 0 elsewhere. The data is represented by b, and is either +1 or - 1. The signal is filtered by a low-

pass RC filter with impulse response

h(t) = ae-u(t),

where u(t) is one for t < 0 and is 0 otherwise. The filter output is sampled every T seconds.

128

(a) Find an expression for the output of the filter at time in terms of bo, b_1, b_2, ...

(b) Suppose that bo = +1. Find the largest and smallest possible value (over all possible data sequences except bo) of the sampled

output.