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1、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0.4，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)/双线性法设计低通滤波器%N-The order of the filter%Apripple in the passband%Ast-a stopband Rs dB down from the peak value in the passband%Wpthe passband widthbe,ae=ellip(3,
2、0.6,32,0.4);hellip=dfilt.df2(be,ae);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=dfilt.df2(b,a);/级联hoverall=cascade(hallpass,hellip);hFVT=fvtool(hellip,hoverall);set(hFVT,Filter,hellip,hoverall);legend(hFVT,Lowpass Elliptic filter,Compensated filter);/添
3、加图例的标注clear;num1,den1=ellip(3,0.6,32,0.4);GdH,w=grpdelay(num1,den1,512);plot(w/pi,GdH); gridxlabel(omega/pi); ylabel(Group delay, samples);F=0:0.001:0.4;g=grpdelay(num1,den1,F,2); % Equalize the passbandGd=max(g)-g;% Design the allpass delay equalizernum2,den2=iirgrpdelay(6,F,0,0.4,Gd);GdA,w = grpde
4、lay(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);pl
5、ot(w,20*log(abs(h),grid;3已知系统的系统函数为： 1212340.5()3.281.zzHz 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-Transformnum = 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，
6、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0.5dBp43dBs和 绘制所设计的滤波器增益响应。7 ra0.35 ras%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
7、/pi,20*log10(abs(h);grid;xlabel(omega/pi); ylabel(Gain);title(Type I Chebyshev Highpass Filter);clear;%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)subplo
8、t(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(0.4.5)2jnxne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-
9、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： 11120.6.8()0.23.24(4)Hzzzz用 MATLAB 求系统 z 变换的有理形式，并写出有理形式
10、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120.4,0.6pp，通带波纹为 0.6dB，最小阻带衰减为120.3,7ss35dB。绘制所设计的滤波器增益响应。% Design of IIR Butterworth Bandpass FilterWp =0.4 0.6;Ws = 0.3 0.7;Rp = 0.6;Rs = 35;N,Wn = buttord(Wp, Ws, Rp, Rs);b,a = butter
11、(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。2(0.9)nxn=0:23;x=2*0.9.n;stem(n,x,.);grid on;ylabel(Amplitude);xlabel(Time index);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
12、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
13、;xlabel(Frequency, Hz); ylabel(Gain, dB);11已知系统的系统函数为：1212340.5()3.281.zzHz 用 MATLAB 的 impz 函数求 hn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);stem(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 0.35，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。%ellip(N
14、,Ap,Ast,Wp)%N-The order of the filter%Apripple in the passband%Ast-a stopband Rs dB down from the peak value in the passband%Wpthe passband widthbe,ae=ellip(5,0.8,35,0.35);hellip=dfilt.df2(be,ae);f=0:0.001:0.4;g=grpdelay(hellip,f,2);g1=max(g)-g;b,a,tau=iirgrpdelay(10,f,0 0.4,g1);%the first parameter
15、 above is the order of the allpasshallpass=dfilt.df2(b,a); hoverall=cascade(hallpass,hellip);hFVT=fvtool(hellip,hoverall);set(hFVT,Filter,hellip,hoverall);legend(hFVT,Lowpass Elliptic filter,Compensated filter);clear;num1,den1=ellip(5,0.8,35,0.35);GdH,w=grpdelay(num1,den1,512);plot(w/pi,GdH); gridxlabel(omega/pi); ylabel(Group delay, samples);F=0:0.001:0.4;g=grpdelay(num1,den1,F,2); % Equalize the passbandGd=max(g)-g;% Design the allpass delay equalizernum2,den2=iirgrpde
