MATLAB40道题与答案修正版

1、操作方法：首先点击FileNewM-File ,输入相应代码，然后点击运行按钮 喧 即可。P1,已知两序列 xn = 0.8nun-un-5, hn =1,1,1,1,)计算两序列的卷积并绘制其波形。%function a1for i=1:5x(i)=0.8A(i-1);endh=1 1 1 1 1;y=conv(x,h)m=0:8;stem(m,y,f川ed)P2。已知复指数序列xn =1.2e(112)n ,绘制20点该序列的实部和虚部。n=0:19;x=1.2*exp(1.5+j*2)*n);subplot(211);stem(n,real(x);ylabel(real part);xl

2、abel(n);legend(xn);subplot(212);stem(n,imag(x);ylabel(imag part);xlabel(n);legend(xn);P3.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(0.5) n，加性噪声信号dn为随机序列，幅度0.4,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 FilteringN = 5;R = 40;a = 0.8*rand(1,R)-0.4;b = round(a); % Generate impulse noise m =

3、 0:R-1;s =3*m.*(0.5.Am); % Generate signalx = s + b; % Impulse noise corrupted signaly = medfilt1(x,N); % Median filtering subplot(2,1,1) stem(m,x);xlabel(n);ylabel(Amplitude);title(Impulse Noise Corrupted Signal);subplot(2,1,2)stem(m,y);xlabel(n);ylabel(Amplitude);title(Output of Median Filter);P4.

4、已知序列 x1n=2.2,3,1.5,4.2,1.8, x2n= 0.8,1,1.6,0.8 , xn=x1n ?x2n(卷积)， 分别绘制序列x1n ,x2n和x n的波形。x1=2.3,3,1.5,4.2,1.8;x2=0,8,1,1,6,0.8;z=conv(x1,x2);t=0:1:4;subplot(311)stem(t,x1);ylabel(x1);pause;t=0:1:3;subplot(312)stem(t,x2);ylabel(x2);pause;w=size(z);n=0:1:(w(2)-1);subplot(313)stem(n,z);ylabel(z);P5.编写4点

5、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.*0.9.Am;x = s + d;plot(m,d,r-,m,s,b-,m,x,g:)xlabel(Time index n); ylabel(

6、Amplitude)legend(dn,sn,xn);pauseb = ones(4,1)/4;y = filter(b,1,x);plot(m,s,r-,m,y,b-)legend(sn,yn);xlabel (Time index n);ylabel(Amplitude)P6,序列xn = 0.8 cos(0.75 n)un-un-8,分别绘制下列序列的波形图：(1) yn = xn+2 ；(2) zn = 2xn + xn 1(3)wn = x2nn=0:1:7;x=0.8.An.*cos(0.75*pi*n);subplot(221);stem(n,x,.);grid;title(xn

7、)y=fliplr(x);ny=fliplr(-(n-2);subplot(222);stem(ny,y,.);grid;title(yn=x-n+2)x1=2*x;x2=x1 0;x3=0 x;y1=x2+x3;subplot(223);stem(0:8,y1,.);grid;title(zn=2xn+xn-1)for i=1:1:4w(i)=x(2*i-1);endsubplot(224);stem(0:3,w,.);grid;title(wn=x2n)P7.序列xn = 0.75nun - un - 3,分别绘制其偶序列分量yn = x0sn和圆周偶序 列分量zn = xccsn的波形图

8、：n=0:1:2;x=0.75*n;xf=fliplr(x);z=zeros(1,length(n)-1);y1=z x;y2=xf z;y=0.5*(y1+conj(y2);subplot(211);stem(-2:2,y,.);title(xcsn)subplot(212)X=fft(x,3);Xre=real(X);xccs=ifft(Xre);stem(0:2,xccs,.);title(xccsn)P8.设原始未受干扰的序列为：sn=3n(0.5) n，加性噪声信号dn为随机序列，幅度0.4, 对该信号测量50次并取样本的整体平均以去除噪声，分别绘制某受干扰的长度为40的测量序列，以

9、及整体平均滤波的输出。% Program 2_13% Generation of the ensemble averageR = 40;m = 0:R-1;s = 3*m.*0.5.Am; % Generate the uncorrupted signald = 0.8*(rand(1,R)-0.5); % Generate the random noisex1 = s+d;xlabel(Time index n);ylabel(Amplitude); title(Noise);subplot(211);stemExl/b,.)for n = 1:40d = 0.8*(rand(1,R)-0.

10、5);x = s + d;x1 = x1 + x;endx1 = x1/ 40;subplot(212);stem(m,x1,c,.);xlabel(Time index n);ylabel(Amplitude); title(Ensemble average);P9,绘制指数序列xn = 0.8nun的幅度谱和相位谱曲线。% Program 3_1% Discrete-Time Fourier Transform Computation% Read in the desired number of frequency samples k = 1000;% Read in the numera

11、tor and denominator coefficientssyms n;d=ztrans(0.8.An);e,f=numden(d);g=sym2poly(e);h=sym2poly(f);n=0:1000;num=0.8.An;den=1;% Compute the frequency responsew = 0:pi/(k-1):pi;h = freqz(num, den, w);% Plot the frequency responsesubplot(211)plot(w/pi,abs(h);gridtitle(Magnitude Spectrum)xlabel(omega八pi)

12、; ylabel(Magnitude)subplot(212)plot(w/pi,angle(h);gridtitle(Phase Spectrum)xlabel(omega八pi); ylabel(Phase, radians)0.5, 0 w n410P10.绘制矩形序列Mn = 甘十 的幅度谱和相位谱曲线。0, 其匕x=0.5*ones(1,11);k = 512;w = 0:pi/(k-1):pi;h = freqz(x, 1, w);% Plot the frequency response subplot(2,1,1) plot(w/pi,abs(h);grid title(Mag

13、nitude Spectrum) xlabel(omega八pi); ylabel(Magnitude) subplot(2,1,2)plot(w/pi,angle(h);gridtitle(Phase Spectrum)xlabel(omega八pi); ylabel(Phase, radians)P11.已知滤波器的差分方程和输入信号分别为：yn= - 6.76195xn+13.456335xn-1 - 6.76195xn- 2xn =cos(0.1n)+2cos(0.4n)un绘制该系统的输入序列和输出序列。a=1;b=-6.76195 13.456335 -6.76195;n=0:10

14、0;x=cos(0.1.*n)+2*cos(0.4.*n);y=filter(b,a,x);y(1,1:2)=0;subplot(211)stem(n,x,.)title(xn)subplot(212)stem(n,y,.)title(yn)1八_ -, 0 n 7P12,绘制8点滑动平均滤波器hn =，8的幅频特性和相频特性。【0,其它h = ones(1,8)/8;H,w = freqz(h, 1,256);subplot(211)plot(w/pi, abs(H);ylabel(Magnitude); xlabel(omega八pi);subplot(212)ph = angle(H)*

15、180/pi;plot(w/pi,angle(H)*180/pi);ylabel(Phase, degrees);xlabel(omega八pi);P13.设计4阶巴特沃兹模拟低通滤波器，其 3-dB截止频率为500冗，绘制滤波器的幅频响 应曲线。N=4;wn=500*pi;num,den=butter(N,wn,s); omega = 0: 0.1: 1200*pi;h = freqs(num,den,omega);plot (omega/(2*pi),20*log10(abs(h);xlabel(Frequency, Hz); ylabel(Gain, dB);P14.设计切比雪夫I型4阶

16、模拟低通滤波器，其3-dB截止频率为500%绘制滤波器的幅 频响应曲线。% Program 4_3% Program to Design Type 1 Chebyshev Lowpass Filter% Read in the filter order, passband edge frequency% and passband ripple in dBN = 4;Fp = 500*pi;% Passband edge frequency in HzRp = 2;% Passband ripple in dB% Determine the coefficients of the transfe

17、r functionnum,den = cheby1(N,Rp,2*pi*Fp,s);% Compute and plot the frequency responseomega = 0: 200: 12000*pi;h = freqs(num,den,omega);plot (omega/(2*pi),20*log10(abs(h);xlabel(Frequency, Hz); ylabel(Gain, dB);P15.设计巴特沃兹模拟高通滤波器，其性能指标为：归一化通带边缘频率为Qp =8000冗rad/s, Cs = 2000冗rad/s通带波纹为0.1dB,最小阻带衰减为40dB。绘制

18、所设计的滤波器增益响 应。N = 4;Wn=500*pi;Rp =0.5;% Determine the coefficients of the transfer functionnum,den = cheby1(N,Rp,Wn,s);% Compute and plot the frequency responseomega = 0: 0.1: 1000*pi;h = freqs(num,den,omega);plot (omega/(2*pi),20*log10(abs(h);xlabel(Frequency, Hz); ylabel(Gain, dB);1,0nW10P16.绘制序列xn

19、=的16点DFT 其匕x=ones(11,1);X=fft(x,16);subplot(2,1,1)stem(0:15,abs(X),.);subplot(2,1,2)stem(0:15,angle(X)/pi*180,.);P17.已知序列 xn = cos(2n rn / N),0 七 n N -1,其中 r = 2, , N = 16。绘制该信号的幅度谱曲线及计算该序列16点的DFTr=2;N=16;n=0:1:15;x=cos(2*pi*r*n/N);k=512;w = 0:pi/(k-1):pi;h = freqz(x, 1, w);subplot(211);plot(w/pi,ab

20、s(h);gridtitle(Magnitude Spectrum)xlabel(omega八pi); ylabel(Magnitude)X=fft(x,16);subplot(212)stem(n,X,.)P18,序列xn =5,4,3,2,1,0, 0n, 5,绘制该序列的8点圆周移位序列yn = x n- 4 A8, 0 w n w 7。x=5 4 3 2 1 0 0 0;y=circshift(x,4);%序列的圆周移位%x待移位序列%m向右移位数%N圆周移位长度%y移位后的输出序列stem(0:7,y,.)一， 八八，-0.5, 0 n 5axis(-1 8 0 6)P19.序列 x

21、n = 5,4,3,2,1,0, 0n5,hn = d,计、0, 县匕算并绘制两序列的8点圆周卷积。首先要在运行的当前目录中定义circonv函数。即新建一个M文件录入以下代码：function y = circonv(x1, x2)% Develops a sequence y obtained by the circular% convolution of two equal-length sequences x1 and x2L1 = length(x1);L2 = length(x2);if L1 = L2, error( Sequences of unequal length), e

22、ndy = zeros(1,L1);x2tr = x2(1) x2(L2:-1:2);for k = 1:L1,sh = circshift(x2tr, k-1);h = x1.*sh;disp(sh);y(k) = sum(h); end保存文件名为circonv.m ,关闭该文件。然后再新建一个新的M文件，输入以下代码：x=5 4 3 2 1 0 0 0;h=0.5 0.5 0.5 0.5 0.5 0.5 0 0;N=8;y=circonv(x,h) stem(0:7,y,.)点击噌按钮。-1, 0 n15P20.已知序列xn= hn = j0 其它，利用DFT计算并绘制两序列的卷积N=1

23、6;L=N+N-1;x=ones(N,1);h=ones(N,1);xe=x zeros(1,L-N);he=h zeros(1,L-N);X=fft(xe,L);H=fft(he,L);Y=X.*H;y=ifft(Y,L); stem(y,.)P21,已知序列 xn = cos(2n n/16) + 2cos(n n/2), 0n15,分别绘制该信号的16点DFT及32点DFT的幅度谱序列和相位谱序列。n=0:15;x=cos(2*pi*n/16)+2*cos(pi*n/2);M=input(Type in the length of the DFT of x,M=);t=0:1:M-1;y

24、1=fft(x,M);subplot(211);stem(t,abs(y1);xlabel(Frequency index k);ylabel(Magnitude);title(Magnitude of the DFT samples);subplot(212);stem(t,angle(y1);xlabel(Frequency index k);ylabel(Phase);title(Phase of the DFT samples);P22.分别绘制序列xn = 0.5n, 0 n 15升 的16点DFT样本的实部和虚部序列分量。0, 其它n=0:1:15;x=05 An;y=fft(x,

25、16);subplot(211) stem(n,real(y);title(real part of y) subplot(212) stem(n,imag(y); title(image part of y)P23.某信号的频谱序列k/8, 0 k 15 Xk =0，其它绘制该序列时域波形k=0:1:15;x=k/8;y=ifft(x,16);t=0:1:15;subplot(211);stem(t,real(y);xlabel(time index n);ylabel(real part of xn);subplot(212);stem(t,imag(y);xlabel(time inde

26、x n); ylabel(image part of xn);P24.某系统的系统函数为H(z) =1+1 - 2z-12+1 -2.5z-11(1-2.5z)2计算该系统的直接形式的结构参数%6_4r=1 2 1;p=2 2.5 2.5;k=1;num, den = residuez(r,p,k)P25.某离散系统的极点为 d = 0.8, p2=0.5 + 0.4j,p3=0.5 0.4j,p4=0.6,零点为z1 = -1,z2 = 2 + 4j, p3 = 2-4j, p4 = 0.5,计算该系统的直接形式的结构参数%6_2z=-1 2+4*j 2-4*j 0.5;p=-0.8 0.5

27、+0.4*j 0.5-0.4*j 0.6;k=1;num, den = zp2tf(z, p, k)1 - 2z-1 4z?1 2.37z, 2.7z 1.6z与 0.41z1、IniP26.计算序列xn =(2)”的z变换，并在z平面上绘制其零极点图clear syms n z a=ztrans(2)An); b=subs(a,z,1/z); c=a+b-1; d=simple(c);disp(Z变换结果:) pretty(d) e,f=numden(d); g=sym2poly(e); h=sym2poly(f);zplane(g,h)的幅频与相频响应P27.绘制IIR系统H (z)num

28、=1 -2 4;den=1 2.37 2.7 1.6 0.41; h w=freqz(num,den);subplot(211) plot(w/pi,abs(h); ylabel(magnitude); xlabel(w);subplot(212) plot(w/pi,angle(h) ylabel(phase);xlabel(w);1-2 .P28.绘制FIR系统H (z) = 1 - 2z + z的幅频与相频响应。num=1 -2 1;den=1;h,w=freqz(num,den);subplot(211);plot(w/pi,abs(h);title(Magnitude respons

29、e) subplot(212);plot(w/pi,angle(h);title(Phase response)P29.计算序列xn = 2nun的z变换，并在z平面上绘制其零极点图syms n;10 x=ztrans(2An) e,f=numden(x); g=sym2poly(e); h=sym2poly(f); zplane(g,h)P30,绘制IIR系统H (z)num=1 -2;den=1 0.5 0 -0.25;h,w=freqz(num,den);subplot(211);plot(w/pi,abs(h);title(Magnitude response) subplot(212

30、);plot(w/pi,angle(h);title(Phase response)P31.绘制FIR系统H (z)num=1 -2 0 -2 1;den=1;h,w=freqz(num,den);subplot(211);plot(w/pi,abs(h);title(Magnitude response) subplot(212);plot(w/pi,angle(h);title(Phase response)1- 2z1 0.5z-0.25z当的幅频与相频响应13一41 - 2z - 2z + z的幅频与相频响应P32.设计切比雪夫I型IIR数字高通滤波器，其性能指标为：通带波纹即=0.5

31、dB ,最小阻带衰减o(s=43dB,通带和阻带边缘频率分别为 p= 0.75 Ttrad和cos=0.35 Ttrad 。绘制 所设计的滤波器增益响应。%9_2disp(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);%注意是Ws在前，另一种方法在9_2中b,a = cheby1(N,Rp,Wn,s);bt,at=lp2hp(b,a,Wp);num,den=bilinear(bt,at,0.5);h,omega

32、= freqz(num,den);plot (omega/pi,20*log10(abs(h);grid;xlabel(omega八pi); ylabel(Gain);title(Type I Chebyshev Highpass Filter);附：9-2% Program 9_2% Type 1 Chebyshev IIR Highpass Filter Design %Wp = 0.75;Ws = 0.5;11Rp = 0.5;Rs = 43;N,Wn = cheb1ord(Wp,Ws,Rp,Rs);b,a = cheby1(N,Rp,Wn, high);h,omega = freqz(

33、b,a,256);plot (omega/pi,20*log10(abs(h);grid;xlabel(omega八pi); ylabel( Gain, dB );title( Type I Chebyshev Highpass Filter);P33设计巴特沃兹数字带通滤波器，其指标要求为：通带边缘频率，p =0.45 0.65,阻 带边缘频率，6s =0.3 0.75,通带波纹为1dB,阻带衰减为40dB,计算该滤波器 的阶数及3dB截止频率。% Program 9_3% Design of IIR Butterworth Bandpass FilterWp =0.45 0.65;Ws =

34、 0.3 0.75;Rp = 1;Rs = 40;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八pi); ylabel(Gain);title(IIR Butterworth Bandpass Filter);disp(N);disp(Wn);P34.设计I型椭圆IIR数字低通滤波器，其性能指标为：通带边缘频率 0.5彳阻带边缘频 率0.75乃通带波纹为1dB,最小阻带衰减为31dB0计算该滤波器的阶数N及3dB

35、截 止频率。% Program 9_1% Elliptic IIR Lowpass Filter DesignWp =0.5;Ws = 0.75;Rp = 1;Rs =31;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八pi); ylabel(Gain, dB);title(IIR Elliptic Lowpass Filter);P35.设计FIR数字低通滤波器，其指标要求为：*=0.3

36、tt ,s =0.4 %阻带衰减为6s=50dB 。用凯塞窗设计，画出具幅频响应曲线。% Program 10_5% Lowpass Filter Design Using the Kaiser Window fpts = 0.3 0.4;12mag = 1 0;dev = 0.003162 0.003162;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;xl

37、abel(omega八pi); ylabel(Gain, dB);P36.设计FIR数字高通滤波器，其指标要求为：cos = 0.4 tt p =j0.6 %阻带衰减为6s=50dB 。用凯塞窗设计，画出具幅频响应曲线。% Program 10_5% Lowpass Filter Design Using the Kaiser Windowfpts = 0.4 0.6;mag = 1 0;dev = 0.003162 0.003162;N,Wn,beta,ftype =kaiserord(fpts,mag,dev);kw = kaiser(N+1,beta);b = fir1(N,Wn,hig

38、h, kw);h,omega = freqz(b,1,512);plot(omega/pi,20*log10(abs(h);grid;xlabel(omega八pi); ylabel(Gain, dB);P37.设计FIR数字带通滤波器，其指标要求为：呼1 = 0.3兀p2 = 0.6兀,s1 = 0.2兀，ws2=0.75，冗阻带衰减为ds = 55dB 。用凯塞窗设计，画出具幅频响应曲线。% Program 10_5% Lowpass Filter Design Using the Kaiser Windowfpts = 0.2 0.3 0.6 0.75;mag = 0 1 0;dev =

39、 0.001778 0.001778 0.001778;N,Wn,beta,ftype =kaiserord(fpts,mag,dev);kw = kaiser(N+1,beta);b = fir1(N,Wn,bandpass, kw);h,omega = freqz(b,1,512);plot(omega/pi,20*log10(abs(h);grid;xlabel(omega八pi); ylabel(Gain, dB);P38.又t 10赫兹申正弦信号以64赫兹的采样速率进行采样，共采得32个样本点，计算其DFT,画出采样序列及DFT的幅度谱序列。% Program of example 11_4% Illustration of DFT Computationclear;% Generate the length-N time-domain sequenceN=32; f=10; fs=64;n=1:N;x=sin(2*pi*f*n/fs);subplot(211)stem(x