Problem 4. Consider two discrete-time LTI systems in series. Overall System x[n]} z[n] y[n] System 1...

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Problem 4. Consider two discrete-time LTI systems in series. Overall System x[n]} z[n] y[n] System 1 System 2 (a) System 1 is described by the following difference equation z[n] = 2n – 1] + r[n] – xn – 6] (1) Determine and plot (stem-plot) the impulse response h (n) of System 1. (b) The frequency response |Hi(w)| of System 1 is the DTFT of the impulse response hi[n]. Plot the magnitude, Hi(w)), of the frequency response of System 1 over - <w<T. (i) Explicitly list all frequencies within the range - <w<a for which H (w) = 0. (ii) Explicitly state the numerical value of H(0). (c) The input signal is obtained from sampling a continuous-time signal as rļn] = 1.(nT.). za(t) = u(t) – u(t – 10) and T, = 4 Determine and plot (stem-plot) the intermediate output 2(n) obtained with this input. (d) The second system is described by the following difference equation. (The input is 2[n] according to the block diagram above, but for purpases of analyzing what the system is doing, you can think of 2[n] as r[n] in the difference equation below.) yin) = uln – 1] + z[n] - 4:[n – 1] (2) %3D Determine and plot the magnit ude, H2(w). of the frequency response of System 2 over -T <w <a. (e) Determine and plot the magnitude, [Y(w)), of the DTFT of the output yn] obtained with the input r[n] defined in part (c). Clearly indicate the frequencies for which Y(w) = 0 over -TSWST. 1 (f) Compute the mmerical value of E, =-Y(w)Pdw. Problem 4. Consider two discrete-time LTI systems in series. Overall System x[n]} z[n] y[n] System 1 System 2 (a) System 1 is described by the following difference equation z[n] = 2n – 1] + r[n] – xn – 6] (1) Determine and plot (stem-plot) the impulse response h (n) of System 1. (b) The frequency response |Hi(w)| of System 1 is the DTFT of the impulse response hi[n]. Plot the magnitude, Hi(w)), of the frequency response of System 1 over - <w<T. (i) Explicitly list all frequencies within the range - <w<a for which H (w) = 0. (ii) Explicitly state the numerical value of H(0). (c) The input signal is obtained from sampling a continuous-time signal as rļn] = 1.(nT.). za(t) = u(t) – u(t – 10) and T, = 4 Determine and plot (stem-plot) the intermediate output 2(n) obtained with this input. (d) The second system is described by the following difference equation. (The input is 2[n] according to the block diagram above, but for purpases of analyzing what the system is doing, you can think of 2[n] as r[n] in the difference equation below.) yin) = uln – 1] + z[n] - 4:[n – 1] (2) %3D Determine and plot the magnit ude, H2(w). of the frequency response of System 2 over -T <w <a. (e) Determine and plot the magnitude, [Y(w)), of the DTFT of the output yn] obtained with the input r[n] defined in part (c). Clearly indicate the frequencies for which Y(w) = 0 over -TSWST. 1 (f) Compute the mmerical value of E, =-Y(w)Pdw.

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MATLAB script clcclose allclear all a b1 0 0 0 0 0 1coefficients of xn a1 1coefficients of zn Impuls... View the full answer