Lecture 10: IIR Filter Designs XILIANG LUO 2014/11 1

Filter Specifications 2

3 1/T=10kHz

IIR: Impulse Invariance 4 If Then

IIR: Impulse Invariance 5 However, any practical continuous-time filter cannot be exactly bandlimited, we will see aliasing! * if continuous time filter approaches zero at high frequencies, aliasing is small!

IIR: Impulse Invariance 6

7 s-plane pole: z-plane pole:

IIR: Impulse Invariance 8 Butterworth filter:

IIR: Impulse Invariance 9

IIR: Bilinear Transform 10

IIR: Bilinear Transform 11 Stability

IIR: Bilinear Transform 12 s-planez-plane

IIR: Bilinear Transform 13

IIR: Bilinear Transform 14

IIR: Bilinear Transform 15

IIR: Bilinear Transform 16 linear phase in continuous time will not give linear phase in discrete time

Butterworth Filter 17 Butterworth lowpass filter: magnitude response is maximally flat in the passband Nth-order Butterworth lowpass filter: the first (2N-1) derivatives of the magnitude-squared function are zero at frequency 0!

Chebyshev Filter 18 Chebyshev lowpass filter: magnitude response is either equiripple in the passband and monotonic in the stopband (I) or monotonic in the passband and equiripple in the stopband (II). Type-1

Elliptic Filter 19 Elliptic lowpass filter: magnitude response is equiripple in both passband and stopband!

Design Comparisons 20 maximum passband gain: 0dB minimum passband gain: -0.3dB maximum stopband gain: -60dB passband edge frequency: stopband edge frequency:

Matlab SPTool 21

Design Comparisons 22 Butterworth Order: 13

Design Comparisons 23 Chebyshev I Order: 8

Design Comparisons 24 Chebyshev I Order: 8

Design Comparisons 25 Chebyshev II Order: 8

Design Comparisons 26 Elliptic Order: 5

Design Comparisons 27 Elliptic