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

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Presentation transcript:

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

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

Windowing 3

4

5 Rectangular window:

Common Windows 6

7

8 Rectangular Window M=50

Common Windows 9 Hamming Window M=50

Common Windows 10 Blackman Window M=50

Comparisons 11

Kaiser Window 12

Kaiser Window 13

Kaiser Window 14

Kaiser Window 15

Kaiser Window 16

Optimal FIR Filter 17 Design Type-1 FIR filter:

Optimal FIR Filter 18

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

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

Optimal FIR Filter 21 Parks-McClellan, MinMax criterion:

Optimal FIR Filter 22

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

Parks-McClellan 24 2(L+2) unknowns

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

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

Parks-McClellan 27

28 Flow Chart of Parks-McClellen

29

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