DSP上机答案final

发布 2022-09-03 08:53:28 阅读 4966

1. 已知3阶椭圆iir数字低通滤波器的性能指标为:通带截止频率0.

4π,通带波纹为0.6db,最小阻带衰减为32db。设计一个6阶全通滤波器对其通带的群延时进行均衡。

绘制低通滤波器和级联滤波器的群延时。

q1_solution

ellip(n,ap,ast,wp)

n---the order of the filter

ap-->ripple in the passband

ast->a stopband rs db down from the peak value in the passband

wp-->the passband width

be,ae]=ellip(3,0.6,32,0.4);

hellip=

f=0:0.001:0.4;

g=grpdelay(hellip,f,2);

g1=max(g)-g;

b,a,tau]=iirgrpdelay(6,f,[0 0.4],g1);

hallpass=

hoverall=cascade(hallpass,hellip);

hfvt=fvtool([hellip,hoverall]);

set(hfvt,'filter',[hellip,hoverall]);

legend(hfvt,'lowpass elliptic filter','compensated filter');

clear;

num1,den1]=ellip(3,0.6,32,0.4);

gdh,w]=grpdelay(num1,den1,512);

plot(w/pi,gdh); grid

xlabel('\omega/\pi');ylabel('group delay, samples');

f=0:0.001:0.4;

g=grpdelay(num1,den1,f,2); equalize the passband

gd=max(g)-g;

design the allpass delay equalizer

num2,den2]=iirgrpdelay(6,f,[0,0.4],gd);

gda,w] =grpdelay(num2,den2,512);

hold on;

plot(w/pi,gdh+gda,'r');

legend('original filter','compensated filter');

2.设计巴特沃兹模拟低通滤波器,其滤波器的阶数和3-db截止频率由键盘输入,程序能根据输入的参数,绘制滤波器的增益响应。

clear;

n=input('type in the order n =

wn=input('type in the 3-db cutoff frequency wn = 模拟频率。

num,den]=butter(n,wn,'s');

w=0:2*wn;

h=freqs(num,den,w);

plot(w,20*log(abs(h)))grid;

3.已知系统的系统函数为:

用matlab进行部分分式展开,并写出展开后的表达式。

partial-fraction expansion of rational z-transform

num = 0 0 1 -0.2 0.5];

den = 1 3.2 1.5 -0.8 1.4];

r,p,k] =residuez(num,den);

disp('residues');disp(r')

disp('poles');disp(p')

disp('constants');disp(k)

4.设计切比雪夫i型iir数字高通滤波器,其性能指标为:通带波纹,最小阻带衰减,通带和阻带边缘频率和绘制所设计的滤波器增益响应。

a4disp('prewapping is done,and t=2');

wp = tan(0.75*pi/2);

ws = tan(0.5*pi/2);

rp = 0.5;

rs = 43;

n,wn] =cheb1ord(ws,wp,rp,rs,'s');

b,a] =cheby1(n,rp,wn,'s');

bt,at]=lp2hp(b,a,wp);

num,den]=bilinear(bt,at,0.5);

h,omega] =freqz(num,den);

plot (omega/pi,20*log10(abs(h)))grid;

xlabel('\omega/\pi');ylabel('gain');

title('type i chebyshev highpass filter');

clear;(没做预畸变)

rp=0.5;

rs=43;

wp=0.75;

ws=0.35;

n,wp]=cheb1ord(wp,ws,rp,rs);

num,den]=cheby1(n,rp,wp,'high');

w=0:pi/1024:pi;

h=freqz(num,den,w);

subplot(2,1,1);

plot(w/pi,abs(h)),grid;title('amplitude in linear scale')

subplot(2,1,2);

plot(w/pi,20*log10(abs(h)))grid;

title('amplitude in log scale')

5.已知复指数序列为:,绘制30点该序列的实部和虚部。

n=0:29;

x=0.2*exp((0.4+1i*0.5)*n);

subplot(211);

stem(n,real(x));

xlabel('n');ylabel('real part');

grid on;

subplot(212);

stem(n,imag(x));

xlabel('n');ylabel('imag part');

grid on;

6.设计切比雪夫i型模拟低通滤波器,其滤波器的阶数,3-db截止频率和通带的波纹由键盘输入,程序能根据输入的参数,绘制滤波器的增益响应。

clear;

n=input(' 滤波器阶数n ='

wn=input(' 截止频率wn =

rp=input('通带波纹rp =

num,den]=cheby1(n,rp,wn,'s');

w=0:5*wn;

h=freqs(num,den,w);

plot(w,20*log10(abs(h)))grid;

xlabel('frequency, hz');ylabel('gain, db');

7.已知系统的系统函数为:

用matlab求系统z变换的有理形式,并写出有理形式的表达式。

r=[1 0.6 1.8];

p=[-3.2 2.4 2.4];

k=0.2;

num, den] =residuez(r,p,k)

8.设计巴特沃兹iir数字带通滤波器,其性能指标为:归一化通带截止频率为,归一化阻带截止频率为,通带波纹为0.6db,最小阻带衰减为35db。绘制所设计的滤波器增益响应。

design of iir butterworth bandpass filter

wp =[0.4 0.6];

ws = 0.3 0.7];

rp = 0.6;

rs = 35;

n,wn] =buttord(wp, ws, rp, rs);

b,a] =butter(n,wn);

h,omega] =freqz(b,a,256);

plot (omega/pi,abs(h));grid;

xlabel('\omega/\pi');ylabel('gain');

title('iir butterworth bandpass filter');

disp(n);

disp(wn);

9.已知指数序列为:,绘制24点该序列。

n=0:23;

x=2*0.9.^n;

stem(n,x,'.

grid on;

ylabel('amplitude');

xlabel('time index/n

10.设计椭圆模拟低通滤波器,其滤波器的阶数,3-db截止频率,通带的波纹和阻带衰减由键盘输入,程序能根据输入的参数,绘制滤波器的增益响应。

clear;

n=input('type in the order n =

wn=input('type in the 3-db cutoff frequency wn =

rp=input('type in the the passband ripple rp =

rs=input('type in the the minimum stopband attenuation rs =

num,den]=ellip(n,rp,rs,wn,'s');

w=0:5*wn;

h=freqs(num,den,w);

plot(w,20*log10(abs(h)))grid;

xlabel('frequency, hz');ylabel('gain, db');

11.已知系统的系统函数为:

用matlab的impz函数求h[n]的前30个样本值。

clc;a=[1 3.2 1.5 -0.8 1.4];

b=[1 -0.2 0.5];

h,t]=impz(b,a,30);

disp(h);

plot(t,h);

12.已知5阶椭圆iir数字低通滤波器的性能指标为:通带截止频率0.35π,通带波纹为0.

8db,最小阻带衰减为35db。设计一个10阶全通滤波器对其通带的群延时进行均衡。绘制低通滤波器和级联滤波器的群延时。

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