FIR Filter Design Concepts

Delve into the world of FIR filter designs with a focus on windowing techniques, common windows like Rectangular, Hamming, and Blackman, Kaiser window optimization, and optimal FIR filter design using the Parks-McClellan algorithm. Explore Fourier series, convergence, and comparisons between various designs for a comprehensive understanding.

• FIR filters
• Windowing techniques
• Filter design
• Digital signal processing
• Fourier series

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Presentation Transcript

1. Lecture 11: FIR Filter Designs XILIANG LUO 2014/11 1

2. Windowing Desired frequency response: Fourier series for a periodic function with period 2pi Convergence of the Fourier series 2

3. Windowing 3

4. Windowing 4

5. Windowing Rectangular window: 5

6. Common Windows 6

7. Common Windows 7

8. Common Windows M=50 Rectangular Window 8

9. Common Windows M=50 Hamming Window 9

10. Common Windows M=50 Blackman Window 10

11. Comparisons 11

12. Kaiser Window 12

13. Kaiser Window 13

14. Kaiser Window 14

15. Kaiser Window 15

16. Kaiser Window 16

17. Optimal FIR Filter Design Type-1 FIR filter: 17

18. Optimal FIR Filter 18

19. Optimal FIR Filter Parks-McClellan algorithm is based on the reformulating the filter design problem as a problem in polynomial approximation. 19

20. Optimal FIR Filter Approx. Error: only defined in interested subintervals of [0, pi] 20

21. Optimal FIR Filter Parks-McClellan, MinMax criterion: 21

22. Optimal FIR Filter 22

23. Parks-McClellan Alternation theorem gives necessary and sufficient conditions on the error for optimality in the Chebyshev or minimax sense! Optimal FIR should satisfy: 23

24. Parks-McClellan 2(L+2) unknowns ??,??are two alternation frequencies 24

25. Parks-McClellan Given set of the extremal frequencies, we can have: 25

26. Parks-McClellan Given set of the extremal frequencies, we can have: Evaluate on other frequencies 26

27. Parks-McClellan 27

28. Flow Chart of Parks-McClellen 28

29. 29

30. 30

31. 1.4 1.2 1 0.8 0.6 0.4 0.2 0 0 0.5 1 1.5 2 2.5 3 3.5 31