matlab上机完美版全解.doc

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%Ap->ripple in the passband%Ast->a stopband Rs dB down from the peak value in the passband%Wp->the passband widthbe,ae=ellip(3,0.6,32,0.4);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 = 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-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，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;%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 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(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');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,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 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 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=iirgrpdelay(10,F,0,0.4,Gd);GdA,w = grpdelay(num2,den2,512);hold on;plot(w/pi,GdH+GdA,'r'); legend('Original Filter','Compensated filter');13编写4点滑动平均滤波器程序。原始未受干扰的序列为：sn=3n(0.8)n, 加性噪声信号dn为随机序列，幅度0.6，受干扰的序列为：xn= sn+ dn，分别绘制长度为40的原始未受干扰的序列，噪声序列和受干扰序列，以及滑动平均滤波器的输出。% Program 2_4% Signal Smoothing by a Moving-Average FilterR = 40;d = 6/5*(rand(1,R)-0.5);m = 0:1:R-1;s =3.*m.*0.8.m;x = s + d;subplot(211);plot(m,d,'r-',m,s,'b:',m,x,'m-')title('The sequence with noise');ylabel('Amplitude')legend('dn','sn','xn');b = ones(4,1)/4;y = fftfilt(b,x);subplot(212);plot(m,s,'r-',m,y,'b-') title('The original sequence & the output sequence');legend('sn','yn');ylabel('Amplitude')14 绘制长度为10点的矩形序列的16点离散傅立叶变换样本的幅度和相位。xn=ones(10,1);Xk=fft(xn,16);Xkf=abs(Xk);Xkp=angle(Xk);subplot(211);stem(0:15,Xkf,'filled');xlabel('Time index/n');ylabel('Magnitude');subplot(212);stem(0:15,Xkp,'filled');xlabel('Time index/n');ylabel('Phase')15已知系统的系统函数为：用MATLAB的filter函数求hn的前20个样本值。num=1,-0.2,0.5;den=1,3.2,1.5,-0.8,1.4;x=1 zeros(1,20-1);y=filter(num, den, x);disp('Coefficients of the power series expansion');disp(y)stem(y)16 利用Hermann公式估计FIR低通滤波器的阶数。该滤波器的性能指标为：通带截止频率为1500Hz，阻带截止频率为1800Hz，通带波纹为0.015，阻带波纹为0.021，抽样频率为5000Hz。% Program 10_1% Estimation of FIR Filter Order Using remezord%clear;fedge = 1500 1800 ;% input('Type in the bandedges = ');mval = 1 0;%input('Desired magnitude values in each band = ');dev = 0.015 0.021;%input('Allowable deviation in each band = ');FT = 5000;%input('Type in the sampling frequency = ');N, fpts, mag, wt = remezord(fedge, mval, dev, FT);d = fdesign.lowpass('n,fp,fst',N,0.6,0.72);design(d);fprintf('Filter order is %d n',N);17 编写长度为5的中值滤波器程序。原始未受干扰的序列为：sn=3n(0.8)n, 加性噪声信号dn为随机序列，幅度0.6，分别绘制长度为40的受干扰序列，以及中值滤波器的输出。% Program 2_5% Illustration of Median Filtering%N = 5;R = 40; b = 6/5*(rand(1,R)-0.5); % Generate impulse noisem = 0:R-1;s = 3*m.*(0.8.m); % Generate signalx = s + b; % Impulse noise corrupted signaly = medfilt1(x,N); % Median filteringsubplot(2,1,1)stem(m,x);axis(0 50 -1 8);grid on;xlabel('n');ylabel('Amplitude');title('Impulse Noise Corrupted Signal');subplot(2,1,2)stem(m,y);grid on;xlabel('n');ylabel('Amplitude');title('Output of Median Filter');18已知16点序列xn的DFT为：绘制序列xn的实部和虚部。Xk=(0:15)/16;xn=ifft(Xk);xnre=real(xn);xnim=imag(xn);subplot(2,1,1);stem(0:15,xnre,'.');grid on;title('The real part of the sequence');subplot(2,1,2);stem(0:15,xnim,'.');grid on;title('The imaginary part of the sequence');19已知系统的系统函数为：用MATLAB测试该系统的稳定性。num=1 -0.2 0.5;den=1 3.2 1.5 0.8 1.4;zplane(num,den);grid on;20. 利用Remez算法设计一个等波纹线性相位FIR低通滤波器。该滤波器的性能指标为：通带截止频率为1500Hz，阻带截止频率为1800Hz，通带波纹为0.015，阻带波纹为0.021，抽样频率为5000Hz。% Program 10_2% Design of Equiripple Linear-Phase FIR Filters%format longfedge = 1500 1800;FT = 5000;mval = 1 0;dev =0.015 0.021;N,fpts,mag,wt = remezord(fedge,mval,dev,FT);b = remez(N,fpts,mag,wt);disp('FIR Filter Coefficients'); disp(b)h,w = freqz(b,1,256);subplot(2,1,1);plot(w/pi,20*log10(abs(h);grid;xlabel('omega/pi'); ylabel('Gain, dB');subplot(2,1,2);plot(w/pi,20*log10(abs(h);grid;axis(0 0.4 -0.7 0.7);xlabel('omega/pi'); ylabel('Gain, dB');title('detail in passband')21. 21.已知序列，计算两个序列的卷积，并绘制序列。clc;clear;x1=2.2 3 -1.5 4.2 -1.8; x2=0.8 -1 1.6 0.8;x=conv(x1,x2) %结果在主界面输出stem(x,'filled');grid on;xlabel('Time index/n');ylabel('Amplitude');title('The output convolution');22. 已知序列xn为，绘制序列xn的DFT和DTFT的幅度。n=0:15;x=cos(pi*n*0.5);X=fft(x);subplot(2,1,1);stem(n,X,'.');title('Magnitude of DFT')xlabel('n'); ylabel('Magnitude')%circulating DTFTk=0:499;w = pi/500*k;X1=x*(exp(-1i*pi/500).(n'*k);magX=abs(X1);subplot(2,1,2);plot(w/pi,magX);title('幅度响应');grid;ylabel('幅度');xlabel('以pi为单位的频率');23. 已知FIR滤波器的系统函数为：用MATLAB将系统函数分解为二次多项式之积，并写出各二次多项式的表达式。clear P=2.4,3.2,1.5,0.8,1.4,3.6,5.2; r=roots(P);%调用函数计算 syms z s1=simple(z-r(1)*(z-r(2); d1=simple(s1./z2)s2=simple(z-r(3)*(z-r(4); d2=simple(s2./z2) s3=simple(z-r(5)*(z-r(6);d3=simple(s3./z2)Q=2.4*d1*d2*d324 已知FIR数字低通滤波器的性能指标为：通带截止频率0.35，阻带截止频率0.45，通带和阻带波纹d = 0.01。设计满足该滤波器的Kaisers窗函数，绘制出Kaisers窗函数的增益响应。clear;fpts=0.35,0.45;mag=1,0;dev=0.01,0.01;N,Wn,beta,ftype=kaiserord(fpts,mag,dev);kw=kaiser(N+1,beta);b=fir1(N,Wn, kw);h,omega=freqz(b,1,512);plot(omega/pi,20*log10(abs(h);grid;xlabel('omega/pi'); ylabel('Gain, dB');25已知系统的频h响特性为： 绘制该系统的幅频特性和相频特性。cleark=500; % number of frequency samples is 500num=1 -.2 .5 2 -.6; %Numerator coefficientsden=1 3.2 1.5 -.8 1.4; %Denominator coefficientsw=0:pi/(k-1):pi; h=freqz(num,den,w); %Compute the frequency responsesubplot(1,2,1)plot(w/pi,abs(h)title('Magnitude Spectrum')xlabel('omega/pi');ylabel('Magnitude')subplot(1,2,2)plot(w/pi,unwrap(angle(h) %unwrapped phase functiontitle('Phase Spectrum')xlabel('omega/pi');ylabel('Phase,radians')sos,g=tf2sos(num,den) 26. 已知序列，基于DFT计算两个序列的卷积，并绘制基于DFT计算得到的。clc;clear;x1=2.2 3 -1.5 4.2 -1.8;x2=0.8 -1 1.6 0.8;n=size(x1,2);m=size(x2,2);X1=fft(x1,n+m-1);X2=fft(x2,n+m-1);X=X1.*X2;x=ifft(X)stem(x,'.');27已知IIR滤波器的系统函数为：用MATLAB将系统函数表示为级联型结构形式，并写出各级联子系统的表达式。（不确定）format short;num = 2,5,1,-3,4,6;den = 1,3,-5,2,-4,3;z,p,k=tf2zp(num,den);sos=zp2sos(z,p,k)28 用Kaisers窗函数设计FIR数字高通滤波器，其滤波器的性能指标为：通带截止频率0.55，阻带截止频率0.45，通带和阻带波纹d =0.04。绘制出该滤波器的增益响应。% Program 10_5% Lowpass Filter Design Using the Kaiser Windowclc%delta_s=50; %阻带衰减delta_p=0.04; %通带衰减%alpha_s=10(-delta_s/20);alpha_p=1-10(-delta_p/20);fpts = 0.45 0.55; %截止频率1，截止频率2mag = 0 1; %截止频率1对应的幅度 截止频率2对应的幅度dev = alpha_p alpha_p; %通带衰减 阻带衰减（线性）N,Wn,beta,ftype=kaiserord(fpts,mag,dev);b = fir1(N,Wn,'high',kaiser(N+1,beta);h,omega = freqz(b,1,512);plot(omega/pi,20*log10(abs(h);grid;xlabel('omega/pi'); ylabel('Gain, dB');29绘制6点滑动平均滤波器的幅频特性和相频特性。h = ones(1,6)/6; H,w = freqz(h, 1, 256);subplot(211)plot(w/pi, abs(H);ylabel('Magnitude'); xlabel('omega/pi');subplot(212)ph = angle(H)*180/pi;plot(w/pi,angle(H)*180/pi);ylabel('Phase, degrees');xlabel('omega/pi');30.原始序列为：sn=3n(0.8)n, 加性噪声dn为随机序列，幅度0.6，受干扰的序列为：xn= sn+ dn，使用重叠相加法实现5点滑动平均滤波器对xn的处理。绘制未受干扰的序列sn和滤波器输出的有噪序列(利用fftfilt函数)。% Program 2_4% Signal Smoothing by a Moving-Average FilterR = 40;d = 6/5*(rand(1,R)-0.5);m = 0:1:R-1;s =3.*m.*0.8.m;x = s + d;subplot(211);plot(m,d,'r-',m,s,'b:',m,x,'m-')title('The sequence with noise');ylabel('Amplitude')legend('dn','sn','xn');b = ones(5,1)/5;y = fftfilt(b,x);subplot(212);plot(m,s,'r-',m,y,'b-') title('The original sequence & the output sequence');legend('sn','yn');ylabel('Amplitude')31已知IIR滤波器的系统函数为：用MATLAB对系统进行并联结构I型和并联结构II型分解。 32. 用海明窗设计多频带FIR滤波器，该滤波器满足如下条件。在频率范围0到0.32p内幅度为0.6，在频率范围0.35p到0.65p内幅度为0.2，在频率范围0.68p到p内幅度为0.8。绘制出该滤波器的幅频特性。 fpts = 0 0.32 0.35 0.65 0.68 1; mval = 0.6 0.6 0.2 0.2 0.8 0.8; b = fir2(100,fpts,mval); h,omega = freqz(b,1,512); plot(omega/pi,abs(h);grid; xlabel('omega/pi'); ylabel('Magnitude');34. 已知系统的系统函数为： 绘制该系统的零极点分布图。 方法一：num=1 -0.2 0.5 2 -0.6; den=1 3.2 1.5 -0.8 1.4;zplane(num,den)35. 已知全通系统的系统函数为：用MATLAB求全通系统进行级联格型结构的乘法器系数。（不确定） num=1 0.4 0.18 -0.2;>> k=poly2rc(num)36.已知有限长序列为：，求该序列的64点离散傅立叶变换Xk，绘制出Xk的幅度。N=64;n=0:1:63;x=sin(25*pi*n/N);%k=512;%w = 0:pi/(k-1):pi;%h = freqz(x, 1, w);%subplot(211);%plot(w/pi,abs(h);grid%title('Magnitude Spectrum')%xlabel('omega/pi'); ylabel('Magnitude')X=fft(x,64);%subplot(212)stem(n,X,'.');grid;设计4阶巴特沃兹模拟低通滤波器，其3-dB截止频率为1，绘制滤波器的增益响应。N = 4;Wn = 1;num,den = butter(N,Wn,'s');h,w = freqs(num,den);plot (w,20*log10(abs(h);xlabel('Frequency, Hz'); ylabel('Gain, dB');title('The 4th-order IIR Butterworth Lowpass Filter ')grid on38. 已知系统的零极点分别如下：求系统的系统函数H(z)。format longzr =2.2 -1+i -1-i 1.4;pr =3.7+2*i 3.7-2*i -2.1-i -2.1+i ;% Transpose zero and pole row vectorsz = zr' p = pr'k = 1;num, den = zp2tf(z, p, k);disp('Numerator polynomial coefficients'); disp(num);disp('Denominator polynomial coefficients'); disp(den);39.设计椭圆IIR数字低通滤波器，其性能指标为：通带截止频率为1000Hz，阻带截止频率为1250Hz，通带波纹为0.4dB，最小阻带衰减为45dB，抽样频率为5000Hz。绘制所设计的滤波器增益响应。 Fp = 1000%input('passband edge in Khz = ');Fs = 1250%input('stopband edge in Khz = ');Ft = 5000%input('Sampling rate in Khz = ');Rp =0.4% input('Passband ripple in dB = ');Rs =45% input('Minimum stopband attenuation in dB = ');Wp=2*Fp/Ft;Ws=2*Fs/Ft;N,Wn = ellipord(Wp,Ws,Rp,Rs);b,a = ellip(N,Rp,Rs,Wn);h,omega = freqz(b,a,256);plot (omega/pi,20*log10(abs(h);grid;xlabel('omega/pi'); ylabel('Gain, dB');title('IIR Elliptic Lowpass Filter');%figure(2);%subplot(2,1,1);%plot(omega/pi,20*log10(abs(h); grid;%axis(0 1 -60 5);%subplot(2,1,2);%plot(omega/pi,20*log10(abs(h); grid;%axis(0 0.4 -0.6 0.2);40.编写总体均值滤波器程序。原始未受干扰的序列为：sn=3n(0.8)n, 加性噪声信号dn为随机序列，幅度0.6，受干扰的序列为：xn= sn+ dn，绘制噪声序列和60次检测结果的总体平均的序列。% Program 2_4% Signal Smoothing by a Moving-Average FilterR = 60;d = 6/5*(rand(1,R)-0.5);m = 0:1:R-1;s =3.*m.*0.8.m;x = s + d;subplot(211);plot(m,d,'r-',m,s,'b:',m,x,'m-')title('The sequence with noise