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1、数字信号处理MATLAB编程作业姓名：白焱 学号：2012001020006M2.2:代码：（以其中一组实例，其他组相同，其他类似情况不在说明）n1=-10:10;xn=5*cos(1.5*pi*n+0.75*pi)+4*cos(0.6*pi*n)-sin(0.5*pi*n);stem(xn);xlabel(n);ylabel(xen);结果：M2.9代码：clear;clc;x = input(Type in the reference sequence = );y = input(Type in the second sequence = );% Compute the correlati
2、on sequencen1 = length(y)-1; n2 = length(x)-1;r = conv(x,fliplr(y);k = (-n1):n2;stem(k,r);xlabel(Lag index); ylabel(Amplitude);v = axis;axis(-n1 n2 v(3:end);结果：Xn自相关序列yn自相关序列wn自相关序列Xn与yn互相关序列Xn与wn互相关序列M3.1代码：rr=input(value of r =);xita=input(value of xita =);fem(1)=0;fem(2)=-2*rr*cos(xita);fem(3)=rr
3、*rr;num = 1;den = fem;% Compute the frequency responsew = 0:pi/(k-1):pi;h = freqz(num, den, w);% Plot the frequency responsesubplot(2,2,1)plot(w/pi,real(h);gridtitle(Real part)xlabel(omega/pi); ylabel(Amplitude)subplot(2,2,2)plot(w/pi,imag(h);gridtitle(Imaginary part)xlabel(omega/pi); ylabel(Amplitu
4、de)subplot(2,2,3)plot(w/pi,abs(h);gridtitle(Magnitude Spectrum)xlabel(omega/pi); ylabel(Magnitude)subplot(2,2,4)plot(w/pi,angle(h);gridtitle(Phase Spectrum)xlabel(omega/pi); ylabel(Phase, radians)结果：（r=0.8,=0.35）M4.1:代码：% Program 4_2% Program to Design Butterworth Lowpass Filter% Type in the filter
5、order and passband edge frequencyN = input(Type in filter order = );Wn = input(3-dB cutoff angular frequency = );% Determine the transfer functionnum,den = butter(N,Wn,s);% Compute and plot the frequency responseomega = 0: 200: 12000*pi;h = freqs(num,den,omega);plot (omega/(2*pi),20*log10(abs(h);xla
6、bel(Frequency, Hz); ylabel(Gain, dB);结果：M4.7：代码：N,Wn = cheb1ord(0.3157894, 1, 0.5, 30,s);B,A = cheby1(N,0.5, Wn,s);num,den = lp2bs(B,A,2*pi*sqrt(700)*106, 2*pi*15e6);figure(1)omega = 0:0.01:10;h = freqs(B,A,omega);gain = 20*log10(abs(h);plot(omega, gain); grid; axis(0 4 -70 5);xlabel(Omega); ylabel(
7、Gain, dB);title(Analog Lowpass Filter);figure(2)omega = 0:10000:160e6*pi;h = freqs(num,den,omega);gain = 20*log10(abs(h);plot(omega/(2*pi), gain); grid; axis(0 80e6 -70 5);xlabel(Frequency in Hz); ylabel(Gain, dB);title(Analog Bandstop Filter);结果：M5.2:代码：clear;clc;g=input(输入序列gn = );h=input(输入序列hn =
8、 );Y=fft(g).*fft(h);y=ifft(Y);disp(y =);disp(y);结果：(a):(b):(c):M5.8:代码：clear;clc;X = 11 8-i*2 1-i*12 6+i*3 -3+i*2 2+i 15;disp(Xk = );disp(X);k = 8:12; XF(k)=conj(X(mod(-k+2,12);XF = X XF(8:12);x = ifft(XF);disp(xn = )disp(x);结果：M5.9:代码：n=0:255;x = 0.1*n.*exp(-0.03*n);figureplot(n,x);axis(0 255 0 1.3
9、);xlabel(n);ylabel(Amplitude);title(Original signal);z = zeros(1,50) ones(1,156) zeros(1,50);y = 4*rand(1,256)-1;YF = z.*fft(y);yinv = ifft(YF);s = x + yinv;figureplot(n,s);axis(0 255 -2 4);xlabel(n);ylabel(Amplitude);title(Noise corrupted signal);zc = ones(1,50) zeros(1,156) ones(1,50);SF = zc.*fft
10、(s);xr = ifft(SF);figureplot(n,xr);axis(0 255 0 1.3);xlabel(n);ylabel(Amplitude);title(Signal after Fourier-domain filtering);结果：M6.1:代码：% Program 6_1% Determination of the Factored Form% of a Rational z-Transform%clear;clc;num = input(Type in the numerator coefficients = );den = input(Type in the d
11、enominator coefficients = );K = num(1)/den(1);Numfactors = factorize(num)Denfactors = factorize(den)disp(Numerator factors);disp(Numfactors);disp(Denominator factors);disp(Denfactors);disp(Gain constant);disp(K);zplane(num,den)结果：(a):(b):M6.3:代码：%协助代码clear;clc;num = input(Type in the num = );den = i
12、nput(Type in the den = );r,p,k = residuez(num,den);disp(r = ); disp(r)disp(p = ); disp(p)disp(k = ); disp(k)% Program 6_4% Partial-Fraction Expansion to Rational z-Transform%clear;clc;r = input(Type in the residues = );p = input(Type in the poles = );k = input(Type in the constants = );num, den = re
13、siduez(r,p,k);disp(Numerator polynomial coefficients); disp(num)disp(Denominator polynomial coefficients); disp(den)结果：(a):(b):(c):(d):M7.1代码;b = 3.8461 -6.3487 3.8461;zi = 0 0;n=0:49;x1 = cos(0.3*n);x2=cos(0.6*n);y = filter(b,1,x1+x2,zi);plot(y,b);hold on;plot(x1,r);hold on;plot(x2,y);axis(5 50 -2
14、2);legend(y,x1,x2);结果：M7.5:代码;clear;clc;num1=input(输入前级系统的分子：);den1=input(输入前级系统的分母：);num2=input(输入后级系统的分子：);den2=input(输入后级系统的分母：);num1fft=fft(num1);num2fft=fft(num2);den1fft=fft(den1);den2fft=fft(den2);numall=ifft(num1fft.*num2fft);denall=ifft(den1fft.*den2fft);k=256;w=0:pi/k:pi;h=freqz(numall,den
15、all,w);subplot(2,1,1);plot(w/pi,abs(h);gridtitle(幅度谱)xlabel(omega/pi);ylabel(幅值)subplot(2,1,2);plot(w/pi,angle(h);gridtitle(相位谱)xlabel(omega/pi);ylabel(弧度)结果:M8.1代码：clear;clc;syms z;hz1=-0.24+0.184*z(-1)+0.4448*z(-2)+1.296*z(-3)+0.4448*z(-4)+0.184*z(-5)-0.24*z(-6);hz2=4-13.6*z(-1)-25.08*z(-2)+77.2*z
16、(-3)-25.08*z(-4)-13.6*z(-5)+4*z(-6);hz3=-0.24+0.184*z(-1)+0.4448*z(-2)+0*z(-3)-0.4448*z(-4)-0.184*z(-5)+0.24*z(-6);hz4=4-13.6*z(-1)-25.08*z(-2)+0*z(-3)+25.08*z(-4)+13.6*z(-5)-4*z(-6);disp(hz1=);disp(factor(hz1);disp(hz2=);disp(factor(hz2);disp(hz3=);disp(factor(hz3);disp(hz4=);disp(factor(hz4);结果：M8
17、.2:代码：clear;clc;num=input(输入分子：);den=input(输入分母：);z,p,k=tf2zp(num,den);m=abs(p);disp(零点);disp(z);disp(极点);disp(p);disp(增益系数);disp(k);sos=zp2sos(z,p,k);disp(二阶节);disp(real(sos);%并联模式r1 p1 k1=residuez(num,den);disp(r1=);disp(r1);disp(p1=);disp(p1);disp(k1=);disp(k1);结果：M8.3:代码：同M8.2结果：M9.1代码：% Program
18、 M9.01N = 5;z, p, k = buttap(N);num, den = zp2tf(z, p, k);% s - s/0.435den = 64.12 90.30 63.58 27.66 7.44 1;num = 0 0 0 0 0 1;% compute z, p, and kz, p, k = tf2zp(num, den);% perform bilinear transformation with T = 2;zd, pd, kd = bilinear(z, p, k, 1/2);% get the digital transfer functionn2, d2 = zp
19、2tf(zd, pd, kd);% get the frequency responseh, w = freqz(n2, d2, 512);figure(1);plot(w/pi, 20*log10(abs(h); grid;axis(0 1 -60 5);xlabel(omega/pi); ylabel(Gain, dB);title(Gain response);figure(2);plot(w/pi, unwrap(angle(h); grid;axis(0 1 -8 1);xlabel(omega/pi); ylabel(Phase, radians);title(Phase resp
20、onse);结果：M9.5:代码;% Problem #M9.05% Impulse invariance methodz, p, k = cheb1ap(5, 0.4);B, A = zp2tf(z, p, k);BT, AT = lp2lp(B, A, 0.628);num, den = impinvar(BT, AT, 1);h, w = freqz(num, den, 512);figure(1);plot(w/pi, 20*log10(abs(h); grid;axis(0 1 -60 5);xlabel(omega/pi); ylabel(Gain, in dB);title(Im
21、pulse Invariance Method);figure(2);plot(w/pi, unwrap(angle(h); gridaxis(0 1 -8 1);xlabel(omega/pi); ylabel(Phase, in radians);title(Impulse Invariance Method);% Bilinear transformation methodz, p, k = cheb1ap(4, 0.4);B, A = zp2tf(z, p, k);BT, AT = lp2lp(B, A, 0.325);num, den = bilinear(BT, AT, 0.5);
22、h, w = freqz(num, den, 512);figure(3);plot(w/pi, 20*log10(abs(h); grid;axis(0 1 -60 5);xlabel(omega/pi); ylabel(Gain, in dB);title(Bilinear Transformation Method);figure(4);plot(w/pi, unwrap(angle(h); gridaxis(0 1 -8 1);xlabel(omega/pi); ylabel(Phase, in radians);title(Bilinear Transformation Method);结果：原型：数字：