南京工程学院通信工程学院数字信号处理第9章.doc

1.（1）n1=0;n2=10;a1=0.5; na1=n1:n2; x1=a1.na1;stem(na1,x1,k);（2）n1=0;n2=10;a1=2; na1=n1:n2; x1=a1.na1;stem(na1,x1,k);（3）n=0:20;x=sin(n*pi/5);stem(n,x);（4）n=0:20;x=cos(n*pi/10-pi/5);stem(n,x);2.（1）a=3,4,1;b=1,1,0;n=32;hn=impz(b,a,n); stem(hn,k);（2）a=5/2,6,10;b=1,0,0;n=32;hn=impz(b,a,n); stem(hn,k);3. n1=0:15;n01=0; h1=(n1-n01)=0; n2=n1;n02=10; h2=(n2-n02)=0; h=(7/8).n1.*(h1-h2);x1=(n1-n01)=0; n2=n1;n03=5;x2=(n2-n03)=0; x=(x1-x2);y=conv(x,h);stem(y);4. b=2,16,44,56,32;a=3,3,-15,18,-12;r p c=residuez(b,a)N=20;n=0:N-1;x=r(1)*p(1).n +r(2)*p(2).nstem(n,x,k);title(用部分分式法求反变换x(n);axis(0,N-1,1.1*min(x),1.1*max(x);5.（1）b=0,2,-1.6,-0.9;a=1,-2.5,1.96,-0.48;rz=roots(b);rp=roots(a);subplot(1,2,1),zplane(b,a);title(系统的零极点分布图);subplot(1,2,2),impz(b,a,20);title(系统的冲激响应);xlabel(n);ylabel(h(n);不是因果稳定系统（2）b=0,0,1,-1;a=1,-0.9,-0.65,0.873;rz=roots(b);rp=roots(a);subplot(1,2,1),zplane(b,a);title(系统的零极点分布图);subplot(1,2,2),impz(b,a,20);title(系统的冲激响应);xlabel(n);ylabel(h(n);因果稳定系统6. b=1,0,0;a=1,-3/4,1/8;n=(0:1000)*pi/1000;h,w=freqz(b,a,n);subplot(2,1,1),plot(n/pi,abs(h);gridaxis(0,1,1.1*min(abs(h),1.1*max(abs(h);ylabel(幅度);subplot(2,1,2),plot(n/pi,angle(h);gridaxis(0,1,1.1*min(angle(h),1.1*max(angle(h);ylabel(相位);xlabel(以pi为单位的频率);7. n1=0:10;n2=0:18;N=20;x1=0.8.n1;x2=0.6.n2;y=cconv(x1,x2,N)8. n=0:20;N=20;x=(0.9*exp(j*pi/3).n;y=fft(x,20)9. fp=3400;Omgp=2*pi*fp; fs=4000;Omgs=2*pi*fs; Rp=3;As=40; n,Omgc=buttord(Omgp,Omgs,Rp,As,s);z0,p0,k0=buttap(n); b0=k0*real(poly(z0); a0=real(poly(p0); freqs(b0,a0);10. T=1;wp=0.2*pi/T;ws=0.3*pi/T;rp=1;rs=15;N,wc=cheb1ord(wp,ws,rp,rs,s);B,A=cheby1(N,rp,wc,s);Bz,Az=impinvar(B,A);H,w=freqz(Bz,Az);plot(w/pi,abs(H);xlabel(频率/pi);ylabel(幅度);11. T=1;Fs=1/T;wp=0.25*pi/T;ws=0.4*pi/T;rp=2;rs=20;Omgp=(2/T)*tan(wp/2);Omgs=(2/T)*tan(ws/2);N,Omgc=ellipord(Omgp,Omgs,rp,rs,s);z0,p0,k0=ellipap(N,rp,rs); ba=k0*real(poly(z0); aa=real(poly(p0); B,A=lp2lp(ba,aa,Omgc);Bz,Az=bilinear(B,A,Fs);H,w=freqz(Bz,Az);plot(w/pi,abs(H);xlabel(频率/pi);ylabel(幅度);12. N=32;window=hamming(N);b=fir1(N-1,0.3 0.5,window); H,w=freqz(b,1)plot(w/pi,abs(H),k);ylabel(幅度);xlabel(频率/pi)13. wc=0.2*pi; N=11;hd= ideallp(wc,N);% 用wc=0.2*pi的理想低通作为逼近滤波器（调用ideallp子程序）wd1=boxcar(N) ; b1=hd.*wd1; % 用矩形窗设计：wd2=hanning(N); b2=hd.*wd2; % 用汉宁窗设计：wd3=blackman(N) ;b3=hd.*wd3; % 用布莱克曼窗设计：H1,w=freqz(b1,1); % 用矩形窗设计的频率特性H2,w=freqz(b2,1); % 用汉宁窗设计的频率特性H3,w=freqz(b3,1); % 用布莱克曼窗设计的频率特性subplot(1,2,1), plot(w,abs(H1),w,abs(H2),:,w,abs(H3),-.);% 绘幅特性legend(矩形窗,汉宁窗,布莱克曼窗)xlabel(omega),ylabel(|H(omega)|)subplot(1,2,2), % 绘分贝幅特性plot(w,20*log10(abs(H1),w,20*log10(abs(H2),:,w,20*log10(abs(H3),-.);legend(矩形窗,汉宁窗,布莱克曼窗)xlabel(omega),ylabel(dB)ideallp子程序：function hd=ideallp(wc,N)tao=(N-1)/2;n=0:(N-1);m=n-tao+eps;hd=sin(wc*m)./(pi*m);14.根据指标要求选择哈明窗wp=0.2*pi; ws=0.3*pi; wc=(ws+wp)/2; tr_width=ws-wp;M=ceil(6.6*pi/tr_width)+1; N=0:1:M-1;alpha=(M-1)/2;n=0:1:(M-1);m=n-alpha + eps;hd=sin(wc*m)./(pi*m);w_ham=(boxcar(M);h=hd.*w_ham;H,w=freqz(h,1,1000,whole);H=(H(1:501);w=(w(1:501);mag=abs(H);db=20*log10(mag+eps)/max(mag);pha=angle(H);grd=grpdelay(h,1,w);delta_w=2*pi/1000;Rp=-(min(db(1:1:wp/delta_w+1);As=-round(max(db(ws/delta_w+1:1:501)subplot(2,2,1);stem(hd);title(理想冲击响应)axis(0 M-1 -0.1 0.3);ylabel(hdn);subplot(2,2,2);stem(w_ham);title(汉明窗);axis(0 M-1 0 1.1);ylabel(wn);subplot(2,2,3);stem(h);title(实际冲击响应);axis(0 M-1 -0.1 0.3);ylabel(hn);subplot(2,2,4);plot(w/pi,db); title(衰减幅度);axis(0 1 -100 10);ylabel(Decibles);15.该题选择了三个非常接近的正、余弦信号，为了将各频率成分区分开来，在满足奈奎斯特定理的条件下确定采样周期。程序如下：fs=400; T=1/fs;%采样频率为400HzTp=0.04; N=Tp*fs;%采样点数NN1=N, 4*N, 8*N; % 设定三种截取长度供调用st=|X1(jf)|;|X4(jf)|;|X8(jf)|;% 设定三种标注语句供调用%矩形窗截断for m=1:3 n=1:N1(m); xn=cos(200*pi*n*T)+sin(100*pi*n*T)+cos(50*pi*n*T);%产生采样序列x(n) Xk=fft(xn,4096); %4096点DFT，用FFT实现 fk=0:4095/4096/T; subplot(3,2,2*m-1) plot(fk,abs(Xk)/max(abs(Xk);ylabel(st(m,:) if m=1 title(矩形窗截取);endend%加hamming窗改善谱间干扰for m=1:3 n=1:N1(m); wn=hamming(N1(m); %调用工具箱函数hamming产生N长hamming窗