a MATLAP project

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EEGR 322 Discrete Systems

MATLAB Project 2

Fall 2017

(Sections 1 and 2: Dr. Arlene Cole-Rhodes/Dr. Mulugeta Dugda)

(Due on Monday November 20, 2017)

Problem 1

Consider the discrete-time LTI system characterized by the following difference equation with input and

initial conditions specified:

y[n] + y[n-1] – 6 y[n-2] = x[n] ,

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with y[0] = 0 and y[1] = 0,

x[n] = (1/2)n u[n-1].

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 = 2, 3, 4.

Problem 2

Consider the causal discrete-time LTI systems characterized by the following difference equations:

1. y[n] = 5.5 x[n] + 0.8 y[n-1]

2. y[n] = x[n] + 0.5 y[n-1] – 0.5 y[n-4] + x[n-3]

3. y[n] = 4.5 x[n] + 2.3 x[n-2] + 4 x[n-4]

For each system above

• Plot the impulse response h[n] for n = 0, 1, 2 , …., 100.

• Determine whether each system is FIR or IIR.

Instructions

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.

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