1. BIEN425 – Lecture 14 By the end of the lecture, you should be able to:
Design and implement IIR filters using frequency transform and bilinear transform
Compare the advantages and disadvantages of IIR filter design strategies (zero-pole versus freq-transform and bilinear transform)

2. In general
This is an alternative way of representing Method 2 from the last lecture. This time, we don’t even need to do partial fraction expansion, the variable in s-domain is simply changed into z-domain.

3. Prove:

4. Bilinear transformation
Simply going between s-plane and z-plane
This is very fun…. A circle becomes a rectangle and a line becomes a arc.
Lecture14.m

6. Frequency warping Given bilinear transformation and s = j2pF
Let’s look at how freq in analog filters (F) can be translated to freq in digital filters (f)
Eq 8.83

7. Learning through example
Building a digital lowpass filter from Chebyshev-I given our digital specs: (Butterworth example 8.8)
f0 = 2.5Hz, f1 = 7.5Hz
dp = 0.1, ds = 0.1 (Could have given Ap and As instead)
Recall the following procedure:
Exam 8.8

8. Step 1a) pre-wrap frequencies to analog specs
Step 1b) compute r, d, minimum order

9. Step 1c) Find poles
Step 1d) Write H(s)

10. Step 2) Determine fs =20hz
Step 3) Re-write into H(z)

11. Another example
Given
Find the resonance frequency of this filter

12. Analog frequency transformation
Design digital HP,BP,BS filters
Always start off with a normalized lowpass filter
Normalized Lowpass Filter (Analog)
Analog Frequency Transformation (Analog)
Bilinear Transformation (Digital)

14. Digital frequency transformation
Normalized Lowpass Filter (Analog)
Bilinear
Transformation (Digital)
Digital Frequency Transformation (Digital)

16. Beware of potential problems
Double check your filter response after design
Stability?
Actual frequency response
Impulse response (check for limit cycles or deadband effects: oscillations even when input has gone to zero)