1. a...... The difference equation of a discrete time system is given by y(n) +

Question

1.

a......

The difference equation of a discrete time system is given by

y(n) + 0.7 y(n-1) + 0.8 y(n-2) = x(n) + 2 x(n-1) + 0.5 x(n-2).

Determine the transfer function of the discrete time system (in z domain) and enter it below.

b.....

Using the roots command, determine the poles and zeroes of the system and enter them below. Is this a stable or unstable system? Briefly justify your answer.

c.....

Assuming a sampling frequency of 500 Hz, compute the graphs of the impulse response, step response, frequency response, and pole-zero constellation of the system and paste the figures below. Be sure to give a title to each figure stating what the figure is showing.

Explanation / Answer

Using roots function

Zeroes :

r = roots(b)

r =

-1.7071
-0.2929

Poles :

>> r = roots(a)

r =

-0.3500 + 0.8231i
-0.3500 - 0.8231i

This is a stable function as all the poles and zeroes lie on the left half plane -ve x axis side

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