Exam/Example Answers

Question 1

If we are given a pole-zero map of a causal filter, how can we distinguish IIR from a FIR filter?

Answer 1

FIR filters will have a pole only at the origin.

IIR filters will have poles at places other than the origin.

Question 2

Given a pole-zero map for a causal filter, how can we identify if it is stable?

Answer 2

All the poles must lie in the unit circle.

Question 3

If we are given a number of pole-zero maps, how can we identify those with the shortest impulse response?

Answer 3

• Disregard any IIR filters - i.e those will non-zero poles
• Look for FIR filters - i.e. those will only one zero pole (impulse response will be of finite length)
• Look to see if any zeroes lie outside the unit circle as this means instability in impulse response (hence takes longer)

Question 4

How do we test the step-response of a transfer function T(s) ?

Answer 4

• Set input X(s)=1/s
• Multiply X(s) = 1/s by the Transfer Function T(s)
• Find Transfer Function as the sum of partial fractions in order to move back into the time-domain

Question 5

The denominator of a transfer function is:

s(s+4)^2

What are the denominators of the partial products?

Answer 5

1. s
2. s+4
3. (s+4)^2