1 BIEN425 – Lecture 14 By the end of the lecture, you should be able to: –Design and implement...

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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)

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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.

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Prove: )1(

)1(2

zT

zs

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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

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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)

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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:

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• Step 1a) pre-wrap frequencies to analog specs

• Step 1b) compute r, d, minimum order

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• Step 1c) Find poles

• Step 1d) Write H(s)

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• Step 2) Determine fs =20hz

• Step 3) Re-write into H(z)

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Another example

• Given

• Find the resonance frequency of this filter

3)1.0(

2.0)(

2

s

ssH

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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)

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Digital frequency transformation

NormalizedLowpass

Filter

(Analog)

BilinearTransformation

(Digital)

DigitalFrequency

Transformation

(Digital)

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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)