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

2. Filter Specifications 2

3. 3 1/T=10kHz

4. IIR: Impulse Invariance 4 If Then

5. 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!

6. IIR: Impulse Invariance 6

7. 7 s-plane pole: z-plane pole:

8. IIR: Impulse Invariance 8 Butterworth filter:

9. IIR: Impulse Invariance 9

10. IIR: Bilinear Transform 10

11. IIR: Bilinear Transform 11 Stability

12. IIR: Bilinear Transform 12 s-planez-plane

13. IIR: Bilinear Transform 13

14. IIR: Bilinear Transform 14

15. IIR: Bilinear Transform 15

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

17. 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!

18. 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

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

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

21. Matlab SPTool 21

22. Design Comparisons 22 Butterworth Order: 13

23. Design Comparisons 23 Chebyshev I Order: 8

24. Design Comparisons 24 Chebyshev I Order: 8

25. Design Comparisons 25 Chebyshev II Order: 8

26. Design Comparisons 26 Elliptic Order: 5

27. Design Comparisons 27 Elliptic