Final answer:
The equivalent impulse response hp(t) for two LTI systems connected in parallel is the sum of their individual impulse responses, h1(t) + h2(t). A plot of hp(t) reflects the combination of the two impulse responses over their non-zero intervals, resulting in a piecewise response from t = -2 to t = 2.
Step-by-step explanation:
The student's question is about determining the equivalent impulse response function hp(t) for two Linear Time-Invariant (LTI) systems connected in parallel, where the impulse response functions are h1(t) = (1 - t) [u(t) - u(t - 1)] and h2(t) = t [u(t + 2) - u(t - 2)]. When systems are connected in parallel, their equivalent impulse response is simply the sum of their individual impulse responses. Hence, the equivalent impulse response hp(t) for the two systems in parallel is the sum h1(t) + h2(t).
To plot hp(t), we must consider the non-zero intervals of each function. The function h1(t) is non-zero from t = 0 to t = 1, where it describes a line from 1 at t = 0 to 0 at t = 1. For the function h2(t), it is non-zero from t = -2 to t = 2, which describes a line increasing from 0 at t = -2 to a maximum at t = 0 and then decreasing to 0 at t = 2. Summing these two will give an overall impulse response that starts at t = -2, peaks at t = 0, and ends by t = 2, with an interruption between t = 0 and t = 1 where the shape is affected by the negative slope of h1(t).