Let hc(t) denote the impulse response of anLTI continuous-time filter and hd [n] the imp...

Let h_c(t) denote the impulse response of anLTI continuous-time filter and hd [n] the impulse response of an LTI discrete-time filter.

(a) If

where a is a positive real constant, determine the continuous-time filter frequency response and sketch its magnitude.

(b) If hd [n] = T h_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 a, determine, as a function of T, the minimum magnitude of the discrete-time filter frequency response.