数字信号处理实验7

Laboratory Exercise 7

DIGITAL FILTER DESIGN

7.1 DESIGN OF IIR FILTERS

Project 7.1 Estimation of IIR Filter Order

Answers:

Q7.1The normalized passband edge angular frequency Wp is -0.2

The normalized stopband edge angular frequency Ws is -0.4

The desired passband ripple Rp is -0.5dB

The desired stopband ripple Rs is -40dB

(1) Using these values and buttord we get the lowest order for a Butterworth lowpass filter

to be - 8

The corresponding normalized passband edge frequency Wn is - 0.2469 or 0.2469pi

(2) Using these values and cheb1ord we get the lowest order for a Type 1 Chebyshev

lowpass filter to be -5

The corresponding normalized passband edge frequency Wn is - 0.2000

(3) Using these values and cheb2ord we get the lowest order for a Type 2 Chebyshev

lowpass filter to be -5

[N, Wn] = cheb2ord(0.2,0.4,0.5,40).

The corresponding normalized passband edge frequency Wn is - 0.4000

(4) Using these values and ellipord we get the lowest order for an elliptic lowpass filter to

be – 4

[N, Wn] = ellipord(0.2,0.4,0.5,40).

From the above results we observe that the Elliptic filter has the lowest order meeting the

specifications.

Q7.2The normalized passband edge angular frequency Wp is - 0.6000

The normalized stopband edge angular frequency Ws is - 0.3429

The desired passband ripple Rp is -1dB

The desired stopband ripple Rs is -50dB

(1) Using these values and buttord we get the lowest order for a Butterworth highpass filter

to be -8

[N, Wn] = buttord(Wp,Ws,Rp,Rs).

The corresponding normalized passband edge frequency Wn is - 0.5647

(2) Using these values and cheb1ord we get the lowest order for a Type 1 Chebyshev

highpass filter to be – 5

[N,Wn] = cheb1ord(Wp,Ws,Rp,Rs).

The corresponding normalized passband edge frequency Wn is - 0.6000

(3) Using these values and cheb2ord we get the lowest order for a Type 2 Chebyshev

highpass filter to be -5

[N,Wn] = cheb2ord(Wp,Ws,Rp,Rs).

The corresponding normalized passband edge frequency Wn is – 0.3429

(4) Using these values and ellipord we get the lowest order for an elliptic highpass filter to

be -4

[N,Wn] = ellipord(Wp,Ws,Rp,Rs).

The corresponding normalized passband edge frequency Wn is –Wn = 0.6000,

From the above results we observe that the Elliptic filter has the lowest order meeting the

specifications.

Project 7.2 IIR Filter Design

A copy of Program P7_1 is given below:

%程序p7.1

%巴特沃斯带阻滤波器的设计

ws=[0.4 0.6];wp=[0.3 0.7];rp=0.4;rs=50;

%估计滤波器的阶数

[N1,wn1]=buttord(wp,ws,rp,rs);

%设计滤波器

[num,den]=butter(N1,wn1,'stop');

%显示传输函数

disp('分子系数是');disp(num);

disp('分母系数是');disp(den);

%计算增益响应

[g,w]=gain(num,den);

%绘制增益响应

plot(w/pi,g);grid

axis([0 1 -60 5]);

xlabel('\omega/\pi');

ylabel('增益，dB');

title('巴特沃斯带阻滤波器的设计');

Answers:

Q7.5The coefficients of the Butterworth bandstop transfer function generated by running Program P7_1 are as follows:

分子系数是

Columns 1 through 6

0.0330 0.0000 0.2972 0.0000 1.1889 0.0000

Columns 7 through 12

2.7741 0.0000 4.1611 0.0001 4.1611 0.0000