FIR FILTER DESIGN 2 Methods FIR Filter Design Windowing MethodFrequency Sampling Method Inverse Discrete Time Fourier Transform / ITFWD Windowing Sampling.

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Digital filters: Design of FIR filters

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Presentation transcript:

FIR FILTER DESIGN

2 Methods FIR Filter Design Windowing MethodFrequency Sampling Method Inverse Discrete Time Fourier Transform / ITFWD Windowing Sampling Inverse Discrete Fourier Transform/IDFT/IFFT

WINDOWING METHOD FIR FILTER DESIGN

Steps 1.Sketch Magnitude Response of Digital Filter as the specification needed 2.Determine the ideal impulse response h i (n) from Magnitude Response 1 st step by Inverse DTFT (look up the table) 3.Determine the delay /symmetrical axis (  ), filter order (N), Filter length (M) 4.Determine and calculate the delayed impulse response in which the delay was determined from 3 rd step, from 0 to N (N-filter order with N+1 filter length) 5.Calculate the coefficient of the window used from 0 to N (N-filter order with N+1 filter length) (given) 6.Multiply the result of 4 th and 5 th step to determine the overall filter coefficient

N-order Windowing Methods FIR Filter Design Inverse Discrete Time Fourier Transform / ITFWD Windowing Filter length : N+1

Steps 1-2 (Several Ideal Magnitude Response) LPF

Steps 1-2 (Several Ideal Magnitude Response) HPF

Steps 1-2 (Several Ideal Magnitude Response) BPF

Steps 1-2 (Several Ideal Magnitude Response) BSF

Steps 1-2 (Several Ideal Magnitude Response) All Pass Filter/Hilbert Transform

Steps 1-2 (Several Ideal Magnitude Response) Differensiator

Steps 3 Determining , N (Filter Order), M (Filter length)

Steps 4 Calculating h i (n-  )

Steps 5 Calculating w(n)

Steps 6 Calculating h(n)=h i (n)w(n)

Latihan  Diketahui suatu filter dengan respon berikut 1. Rancanglah filter tsb ! 2. Ceklah filter hasil perancangan

SAMPLING FREQUENCY METHOD FIR FILTER DESIGN

18 Desired real-valued frequency response: Frequency-Sampling Method: Basic Principle Approximation error: Samples of Approximation of ideal frequency response:

19 Example: magnitude responses (linear scale) Task of a): transition region width= Task of b): transition region width= k=0k=1k=2k=3 k=5 k=6k=7 a) k=4 b) k=4

2 Methods FIR Filter Design Windowing MethodFrequency Sampling Method Inverse Discrete Time Fourier Transform / ITFWD Windowing Sampling Inverse Discrete Fourier Transform/IDFT/IFFT

Sampling Frequency Formula 21 N = Length of FIR filter