BIEN425 – Lecture 14

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)

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.

Prove:

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

Frequencywarping • 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)

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:

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

Step 1c) Find poles • Step 1d) Write H(s)

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

Another example • Given • Find the resonance frequency of this filter

Analog frequency transformation • Design digital HP,BP,BS filters • Always start off with a normalized lowpass filter NormalizedLowpassFilter(Analog) AnalogFrequencyTransformation(Analog) BilinearTransformation(Digital)

Digital frequency transformation NormalizedLowpassFilter(Analog) Bilinear Transformation(Digital) DigitalFrequencyTransformation(Digital)

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)

BIEN425 – Lecture 14