数字信号处理第三章(matlab).doc

%计算N点的DFTfunction Xk = dft(xn,N)n=0:1:N-1;k=0:1:N-1;WN=exp(-j*2*pi/N);nk=n*k;WNnk=WN.nk;Xk=xn*WNnkEnd%计算N点的逆DFTfunction xn = idft(Xk,N)n=0:1:N-1;k=0:1:N-1;WN=exp(-j*2*pi/N);nk=n*k;WNnk=WN.(-nk);xn=(Xk*WNnk)/N;end%循环移位函数functiony=cirshift(x,m,N)if length(x)N error( N必须大于等于x(n)的长度)endx=x zeros(1,N-length(x);n=0:N-1;n=mod(n-m,N);y=x(n+1);%计算序列x1(n) 和x2(n)之间的N点循环卷积函数functiony=circonvt(x1,x2,N)if length(x1)N error( N必须大于等于x1的长度)endif length(x2)N error( N必须大于等于x2的长度)endx1=x1 zeros(1,N-length(x1);x2=x2 zeros(1,N-length(x2);m=0:1:N-1;x2=x2(mod(-m,N)+1);H=zeros(N,N);for n=1:1:N H(n,:)=cirshift(x2,n-1,N);endy=x1*H;例3.2（P139） x=1,1,1,1,1,1;n=0:5; k=-200:200;w=(pi/100)*k; X=x*(exp(-j*pi/100).(n*k); magX=abs(X);angX=angle(X)*180/pi; figure(1) subplot(2,1,1);plot(w/pi,magX); axis(-1 1 0 6);grid; title(DTFT的幅度);xlabel(以pi为单位的频率);ylabel(幅度); subplot(2,1,2);plot(w/pi,angX);grid; axis(-1 1 -200 200);title(DTFT的相位); xlabel(以pi为单位的频率);ylabel(相位); N=6; X=dft(x,N); magX=abs(X);phaX=angle(X)*180/pi; k=0:5; figure(2) subplot(2,1,1);stem(k,magX); title(DFT的幅度);xlabel(k); subplot(2,1,2);stem(k,phaX); title(DFT的相位);xlabel(k);Xk = Columns 1 through 5 6.0000 -0.0000 - 0.0000i -0.0000 - 0.0000i 0 - 0.0000i 0.0000 - 0.0000i Column 6 0.0000 - 0.0000i例3.3（P141） n=0:9;x=0.8*cos(0.47*pi*n)+0.4*cos(0.53*pi*n); N=10; X=dft(x,N); magX=abs(X),angX=angle(X) k=0:9; subplot(2,1,1);stem(k,magX);title(DFT的幅度); xlabel(k); subplot(2,1,2);stem(k,angX);title(DFT的相位); xlabel(k);Xk = Columns 1 through 5 1.1611 1.2250 + 0.7289i 2.0522 + 3.5598i 0.9030 - 2.9037i 0.8213 - 0.6744i Columns 6 through 10 0.8360 - 0.0000i 0.8213 + 0.6744i 0.9030 + 2.9037i 2.0522 - 3.5598i 1.2250 - 0.7289imagX = 1.1611 1.4254 4.1090 3.0409 1.0627 0.8360 1.0627 3.0409 4.1090 1.4254angX = 0 0.5367 1.0478 -1.2693 -0.6875 -0.0000 0.6875 1.2693 -1.0478 -0.5367例3.4（P143） n=0:10;x=8*(0.8).n;N=11; y=cirshift(x,6,N); subplot(2,1,1);stem(n,x);title(序列x(n); xlabel(n);ylabel(x(n); subplot(2,1,2);stem(n,y);title(x(n)的循环移位); xlabel(n);ylabel(y(n);例3.5（P144） x1=1,2,2;x2=5,4,3,2,1;N=5; y=circonvt(x1,x2,N)y =11 16 21 16 11例3.6（P144） n=0:9;x1=(0.8).n; n=0:6;x2=exp(-n);N=10; y=circonvt(x1,x2,N)y = 1.0905 1.2008 1.0815 0.9096 0.7440 0.6012 0.4832 0.3866 0.3093 0.2474例3.7（P146） N=32;fs=100;T=1/fs; n=0:N-1;r=n*T;x=r.*exp(r); X=fft(x,N); magX=abs(X),phaX=angle(X) subplot(3,1,1);stem(n,x);axis(0 32 0 1); xlabel(n);title(序列x(n); k=0:N-1; subplot(3,1,2);stem(k,magX);axis(0 32 0 8); xlabel(k);ylabel(DFT的幅度); subplot(3,1,3);stem(k,phaX);axis(0 32 -4 4); xlabel(k);ylabel(DFT的相位);magX = Columns 1 through 10 6.1357 2.2215 1.1182 0.7518 0.5704 0.4630 0.3929 0.3441 0.3087 0.2824 Columns 11 through 20 0.2625 0.2475 0.2363 0.2281 0.2226 0.2194 0.2183 0.2194 0.2226 0.2281 Columns 21 through 30 0.2363 0.2475 0.2625 0.2824 0.3087 0.3441 0.3929 0.4630 0.5704 0.7518 Columns 31 through 32 1.1182 2.2215phaX = Columns 1 through 10 0 1.5747 1.7204 1.8347 1.9411 2.0443 2.1459 2.2467 2.3469 2.4467 Columns 11 through 20 2.5463 2.6457 2.7450 2.8442 2.9434 3.0425 3.1416 -3.0425 -2.9434 -2.8442 Columns 21 through 30 -2.7450 -2.6457 -2.5463 -2.4467 -2.3469 -2.2467 -2.1459 -2.0443 -1.9411 -1.8347 Columns 31 through 32 -1.7204 -1.5747例3.8（P148） N=21;L=256;f1=120;f2=140;fs=400;T=1/fs;ws=2*pi*fs;n=0:N-1;x=cos(2*pi*f1*n*T)+cos(2*pi*f2*n*T);X=fftshift(fft(x,L);w=(-ws/2+(0:L-1)*ws/L)/(2*pi);subplot(2,1,1);plot(w,abs(X);ylabel(幅度谱);xlabel(频率(Hz) N=21);axis(-200 200 0 15);N=11;n=0:N-1;x=cos(2*pi*f1*n*T)+cos(2*pi*f2*n*T);X=fftshift(fft(x,L);subplot(2,1,2);plot(w,abs(X);axis(-200 200 0 25);ylabel(幅度谱);xlabel(频率(Hz) N=11);例3.10（P152） n=0:20; x=cos(0.1*pi*n); h=(0.8).n; L=length(x)+length(h)-1; X=fft(x,L); H=fft(h,L); y=ifft(X.*H) subplot(3,1,1);stem(n,x);ylabel(序列x(n);xlabel(n); subplot(3,1,2);stem(n,h);ylabel(序列h(n);xlabel(n); n=0:L-1; subplot(3,1,3);stem(n,real(y); ylabel(卷积结果y(n);xlabel(n);y = Columns 1 through 10 1.0000 1.7511 2.2099 2.3557 2.1936 1.7548 1.0949 0.2881 -0.5785 -1.4139 Columns 11 through 20 -2.1311 -2.6559 -2.9338 -2.9348 -2.6569 -2.1255 -1.3914 -0.5253 0.3888 1.2621 Columns 21 through 30 2.0097 1.5985 1.2700 1.0086 0.8014 0.6383 0.5106 0.4114 0.3345 0.2751 Columns 31 through 40 0.2288 0.1923 0.1626 0.1375 0.1155 0.0952 0.0762 0.0581 0.0410 0.0254 Column 410.0115例3.11（P153） b=0.0181,0.0543,0.0543,0.0181;a=1,-1.7600,1.1829,-0.2781;ch=impseq(0,0,20);n=0:20;h=filter(b,a,ch);x=cos(0.1*pi*n)+0.32*randn(size(n);L=length(x)+length(h)-1;X=fft(x,L);H=fft(h,L);y=ifft(X.*H)subplot(3,1,1);plot(n,x);axis(0 20 -1.5 1.5);ylabel(信号X(n);xlabel(n);subplot(3,1,2);stem(n,h);axis(0 20 -0.5 0.5);ylabel(系统冲激响应h(n);xlabel(n);n=0:L-1;subplot(3,1,3);plot(n,y);axis(0 20 -1.5 1.5);ylabel(x(n)滤波的结果y(n);xlabel(n);y = Columns 1 through 10 0.0130 0.0795 0.2283 0.4246 0.5909 0.6591 0.6050 0.4556 0.2503 -0.0104 Columns 11 through 20 -0.3476 -0.7126 -0.9934 -1.1208 -1.