Assume that the continuous-time signal x_c(t) in Figure is exactly bandlimited and exactly time limited so that

x_c(t) = 0 for t 10 seconds

and?

X_e(j?) = 0 for |?| ? 2? ? 10⁴

While no continuous-time signal can be exactly bandlimited and time limited, the assumption that a signal satisfies both constraints often an excellent approximation and one that we typically rely on in discrete-time processing of continuous-time signals. The continuous-time signal x_c(t) is sampled as indicated in Figure to obtain the sequence x[n], which we want to process to estimate the total area A under x_c(t) as precisely possible. Specify a choice for the impulse response h[n] for the discrete-time system and the largest possible value of T to obtain as accurate an estimate as possible of A. State specifically whether your estimate will be exact or approximate.

Transcribed Image Text:

Discrete-time C/D x[n] Â = estimate of A * (1) system 10 A = L(1) dt.