Embed Size (px)
Citation preview
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 variablein s-domain is simply changed into z-domain.
3
Prove: )1(
)1(2
zT
zs
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
5
6
Frequency warping
• Given bilinear transformation and s = j2F
• Let’s look at how freq in analog filters (F) can be translated to freq in digital filters (f)
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
– p = 0.1, s = 0.1 (Could have given Ap and As instead)
• Recall the following procedure:
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
3)1.0(
2.0)(
2
s
ssH
12
Analog frequency transformation
• Design digital HP,BP,BS filters• Always start off with a normalized lowpass filter
NormalizedLowpass
Filter
(Analog)
AnalogFrequency
Transformation
(Analog)
BilinearTransformation
(Digital)
13
14
Digital frequency transformation
NormalizedLowpass
Filter
(Analog)
BilinearTransformation
(Digital)
DigitalFrequency
Transformation
(Digital)
15
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)
