1 BIEN425 – Lecture 12 By the end of the lecture, you should be able to: –Design and implement IIR filters using zero-pole placement

2 IIR filters If FIR filters are always stable, why bother with IIR?

3 Example: notch filter Notch filter – a special case of bandstop filter where the width of stopband approaches zero Very simply, we can place the zeros at some angles on the unit circle.

4 Where do we put the poles? To control the 3-dB bandwidth, we can simply play the poles at the same angles, but just inside the unit circle Lecture12.m

5 Determine r and b 0 We need r < 1 for stability, but r ≈ 1 for selectivity. Generally, damping decreases as r→1; damping increase as r→0. If we want 3dB passband,  F in width, b 0 can be obtained by setting |H(z 0 )|=1

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8 Comb and inverse comb What is it? To filter harmonic noise from biomedical measurements. For example, fluorescent light Lecture12.m

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10 General procedure Selection of f s Choose corner frequency f c. This corresponds to the corner frequency for lowpass and highpass; resonant frequency for bandpass and notch frequency at bandstop filters Find angles θ for each f c. Select r Place zeros: –Lowpass: -1, -1 (could be multiple depending on order) –Bandpass: -1, 1 (could be multiple depending on order) –Highpass: 1, 1 (could be multiple depending on order) –Bandstop: exp(± θ)