EEGR322 Discrete Systems MATLAB Project 2 Assignment In this project, all the problems (except hand calculations) must be answered using MATLAB. Work with

EEGR322 Discrete Systems MATLAB Project 2 Assignment In this project, all the problems (except hand calculations) must be answered using
MATLAB. Work with your assigned partner from Project 1. Clearly label the axes for all
plotted signals. Your report should include a title page, problem statement, results clearly
presented and a short ‘Conclusion’ section, with MATLAB code provided in the
Appendix. EEGR 322 Discrete Systems
MATLAB Project 2
Spring 2019
(Sections 1 and 2: Dr. Arlene Cole-Rhodes/Dr. Mulugeta Dugda)
Due on Tuesday, April 23, 2019
Instruction:
In this project, all the problems (except hand calculations) must be answered using
MATLAB. Work with your assigned partner from Project 1. Clearly label the axes for all
plotted signals. Your report should include a title page, problem statement, results clearly
presented and a short ‘Conclusion’ section, with MATLAB code provided in the
Appendix.
Problem 1
Consider the discrete-time LTI system characterized by the following difference equation
with input and initial conditions specified:
y[n] – 1.5 y[n-1] – y[n-2] = x[n], with y[0] = 1 and y[-1] = 0, x[n] = (0.5)n u[n-1].
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Write a MATLAB program to simulate this difference equation.
You may try the commands ‘filter’ or ‘filtic’, or create a loop to compute the values
recursively.
Printout and plot the values of the input signal, x[n] and the output signal, y[n] over the
range 1 ≤ n ≤ 10.
Solve this difference equation by hand using the classical method.
Verify that the values of the output signal, y[n] produced by MATLAB are the same as
those calculated by hand for the values of n = 1, 2, 3.
Problem 2
Consider the causal non-linear discrete-time system characterized by the following
difference equation:
2y[n] = y[n-1] + x[n] / y[n-1]
If we use as input x[n] to this system (algorithm) a step function of amplitude P (i.e.
x[n]=P u[n]), then y[n] will converge after several iterations to the square root of P.
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Write a MATLAB program that implements the above recursion to compute the square
roots of 25, 9, 3, and 2.
How many iterations does it take to converge to the true value starting at y[-1] = 0.2?

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