实验五

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Laboratory Exercise 5 (4 class hours)

FIR AND IIR F ILTERS

Project 4.1 Approximating Ideal Low pass filter The impulse response of anideal low pass filter is

)(sinc )sin(1][1111ΩΩ=Ω=n n n n h π

π, where 1Ω is the cut-off frequency.

Select an arbitrary value of 1Ω, truncate ][1n h with certain number of samples N , and shift it in order to get a casual impulse response ][n h . Plot the frequency response (both magnitude and phase) of ][n h through using the …freqz? function or your own …dtft? function.

Project 4.2 Shift to Band pass filter and High pass filter

Multiply the truncated version of ][1n h in Project 4.1 by )cos(0n Ω, )sin(0n Ω, and n j e 0Ω, and then shift it to get a casual sequence, the corresponding filter will be band pass or high pass (π=Ω0) filters, which depends on the choice of 0Ω. Compare the frequency responses of the three methods.

Project 4.4 User-defined function for IIR filter design

Program your own function for 1st order Butterworth digital IIR filter design, using the Bilinear Transformation with prewarping.

The syntax is “[b,a] = iirbutter(fp1,fs,N)”

Inputs:

1. fp1, the 3dB frequency of the 1st order Butterworth filter in Hz.

2. fs , the sampling frequency

3. N , the number of samples of the frequency response

Outputs:

1. vector b , the coefficients of k b , in ascending powers of 1-z

2. Vector a , the coefficient of k a , in ascending powers of 1-z i.e., 1,)(01101

10=++=--a z

a a z

b b Z H 3. plots of the frequency responses:

1) magnitude response

)Hz (|~)(|f f H 2) phase response

)Hz (~(f f ）θ

Example (see e.g. 10.4 on pp. 393)

[b,a]=iirbutter(2000/(2*pi),1500,100);

Project 4.5 (only for practice) use the “[numd,dend] = bilinear(num,den,fs,fp)” function to obtain the filter coefficients, search for “bilinear” in the help browser for detailed information.

Date:2017年12月22日Signature: