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Problem 1: Consider a DT-LTI system where the output y[n] is a linear superposition of time- shifted input signal x[n]: y[n] = 3x[n-1] − x[n - 4] (a) (10 pts) Draw a block diagram that can implement such a system. Your block diagram should contain delay and summation operators / blocks. (b) (10 pts) Determine the impulse response function h[n] of this DT system. (c) (10 pts) Determine whether this system is stable. (d) (10 pts) Derive a closed-form expression for the eigenvalue (or transfer function) H(z) of this system. (e) (10 pts) Derive a closed-form expression for the frequency response H(ejw) of the system and use Matlab to generate its Bode plot. Include both the plot and the Matlab script in your submission. (f) (10 pts) Suppose the input signal is given by x[n] = e−0.2n cos(0.3´n) u[n]. Derive a closed-form expression for the Fourier transform X (ejw) of the input signal. (g) (10 pts) Use Matlab to generate the Bode plot of X(ejw). Include both the plot and the Matlab script in your submission. (h) (10 pts) Determine the Fourier transform Y(ejw) of the output signal y[n]. (i) (10 pts) Use Matlab to generate the Bode plot of Y(ejw). Include both the plot and the Matlab script in your submission.

Problem 1: Consider a DT-LTI system where the output y[n] is a linear superposition of time- shifted input signal x[n]: y[n] = 3x[n-1] − x[n - 4] (a) (10 pts) Draw a block diagram that can implement such a system. Your block diagram should contain delay and summation operators / blocks. (b) (10 pts) Determine the impulse response function h[n] of this DT system. (c) (10 pts) Determine whether this system is stable. (d) (10 pts) Derive a closed-form expression for the eigenvalue (or transfer function) H(z) of this system. (e) (10 pts) Derive a closed-form expression for the frequency response H(ejw) of the system and use Matlab to generate its Bode plot. Include both the plot and the Matlab script in your submission. (f) (10 pts) Suppose the input signal is given by x[n] = e−0.2n cos(0.3´n) u[n]. Derive a closed-form expression for the Fourier transform X (ejw) of the input signal. (g) (10 pts) Use Matlab to generate the Bode plot of X(ejw). Include both the plot and the Matlab script in your submission. (h) (10 pts) Determine the Fourier transform Y(ejw) of the output signal y[n]. (i) (10 pts) Use Matlab to generate the Bode plot of Y(ejw). Include both the plot and the Matlab script in your submission.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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Problem 1: Consider a DT-LTI system where the output y[n] is a linear superposition of time- shifted input signal x[n]: y[n] = 3x[n-1] − x[n - 4] (a) (10 pts) Draw a block diagram that can implement such a system. Your block diagram should contain delay and summation operators / blocks. (b) (10 pts) Determine the impulse response function h[n] of this DT system. (c) (10 pts) Determine whether this system is stable. (d) (10 pts) Derive a closed-form expression for the eigenvalue (or transfer function) H(z) of this system. (e) (10 pts) Derive a closed-form expression for the frequency response H(ejw) of the system and use Matlab to generate its Bode plot. Include both the plot and the Matlab script in your submission. (f) (10 pts) Suppose the input signal is given by x[n] = e−0.2n cos(0.3´n) u[n]. Derive a closed-form expression for the Fourier transform X (ejw) of the input signal. (g) (10 pts) Use Matlab to generate the Bode plot of X(ejw). Include both the plot and the Matlab script in your submission. (h) (10 pts) Determine the Fourier transform Y(ejw) of the output signal y[n]. (i) (10 pts) Use Matlab to generate the Bode plot of Y(ejw). Include both the plot and the Matlab script in your submission.
Transcribed Image Text:Problem 1: Consider a DT-LTI system where the output y[n] is a linear superposition of time- shifted input signal x[n]: y[n] = 3x[n-1] − x[n - 4] (a) (10 pts) Draw a block diagram that can implement such a system. Your block diagram should contain delay and summation operators / blocks. (b) (10 pts) Determine the impulse response function h[n] of this DT system. (c) (10 pts) Determine whether this system is stable. (d) (10 pts) Derive a closed-form expression for the eigenvalue (or transfer function) H(z) of this system. (e) (10 pts) Derive a closed-form expression for the frequency response H(ejw) of the system and use Matlab to generate its Bode plot. Include both the plot and the Matlab script in your submission. (f) (10 pts) Suppose the input signal is given by x[n] = e−0.2n cos(0.3´n) u[n]. Derive a closed-form expression for the Fourier transform X (ejw) of the input signal. (g) (10 pts) Use Matlab to generate the Bode plot of X(ejw). Include both the plot and the Matlab script in your submission. (h) (10 pts) Determine the Fourier transform Y(ejw) of the output signal y[n]. (i) (10 pts) Use Matlab to generate the Bode plot of Y(ejw). Include both the plot and the Matlab script in your submission.
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