Let h_c(t) denote the impulse response of a linear time-invariant continuous-time filter and h_d[n] the impulse response of a linear time-invariant discrete-time filter.

(a) If

(b) If h_d[n] = Th_c(nT) with h_c(t) as in part (a), determine the discrete-time filter frequency response and sketch its magnitude.

(c) For a given value of α, determine, as a function of T. the minimum magnitude of the discrete-time filter frequency response.

Transcribed Image Text:

-at h.(1) : 0. = : 0. I < 0,