FIR FILTER DESIGN 2 Methods FIR Filter Design

FIR FILTER DESIGN

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

WINDOWING METHOD FIR FILTER DESIGN

Steps 1. 2. 3. 4. 5. 6. Sketch Magnitude Response of Digital Filter as the specification needed Determine the ideal impulse response hi(n) from Magnitude Response 1 st step by Inverse DTFT (look up the table) Determine the delay /symmetrical axis ( ), filter order (N), Filter length (M) 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) Calculate the coefficient of the window used from 0 to N (N-filter order with N+1 filter length) (given) 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 hi(n- )

Steps 5 Calculating w(n)

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

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

SAMPLING FREQUENCY METHOD FIR FILTER DESIGN

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

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

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

Sampling Frequency Formula 21 N = Length of FIR filter