MATLAB编程Zero-poleplane.doc

Projects 1: Part AProblem 1 for the following system: y(n)+ay(n-1)=x(n); where (a) a=0.9; (b) a=-0.9(a)Zero-pole plane, impulse response, |H(w)| and angle H(w): in figure 1. Figure 1.DFT of the impulse response (magnitude and angular spectrum): in figure 2. Figure 2.Comparison between DFT and DTFT:When N=10: in figure 3. Figure 3.When N=30: in figure 4 Figure 4.When N=50: in figure 5. Figure 5.(b)Zero-pole plane, impulse response, |H(w)| and angle H(w): in figure 6. Figure 6.DFT of the impulse response (magnitude and angular spectrum): in figure 7. Figure 7.Comparison between DFT and DTFT:When N=10: in figure 8. Figure 8.When N=30: in figure 9. Figure 9.When N=50: in figure 10. Figure 10.Problem 2: repeat steps above for the following system:H (Z) =Where (a) 0=/8 and r=0.95;(b) 0=/4 and r=0.95;(c) 0=/8 and r=0.99;(a)Zero-pole plane, impulse response, |H (w)| and angle H (w): in figure 11. Figure 11.DFT of the impulse response (magnitude and angular spectrum): in figure 12. Figure 12.Comparison between DFT and DTFT:When N=10: in figure 13. Figure 13.When N=30: in figure 14. Figure 14.When N=50: in figure 15. Figure 15. (b)Zero-pole plane, impulse response, |H(w)| and angle H(w): in figure 16. Figure 16.DFT of the impulse response (magnitude and angular spectrum): in figure 17. Figure 17.Comparison between DFT and DTFT:When N=10: in figure 18. Figure 18.When N=30: in figure 19. Figure 19.When N=50: in figure 20. Figure 20.(c)Zero-pole plane, impulse response, |H (w)| and angle H (w): in figure 21. Figure 21.DFT of the impulse response (magnitude and angular spectrum): in figure 22. Figure 22.Comparison between DFT and DTFT:When N=10: in figure 23. Figure 23When N=30: in figure 24. Figure 24.When N=50: in figure 25. Figure 25.Problem 1:(a) a=0.91（Z-P plane&impulse response&DTFT） b=1; a=1 0.9; pul=1 zeros(1,59); subplot(221) zplane(b,a) title(zero-pole plane) subplot(222) h1=impz(b,a,60); stem(h1) title(impulse response) subplot(223) H,w=freqz(b,a,whole); plot(w,abs(H) title(|H(w)|) xlabel(w) subplot(224) plot(w,angle(H) title(angle H(w) xlabel(w)2(DFT) b=1; a=1 0.9; L=100; NFFT=2nextpow2(L); N=10; h1=impz(b,a,N); H,w=freqz(b,a,NFFT); y=fft(h1,NFFT); magY=abs(y); phaY=angle(y); subplot(221) plot(w,magY) title(magnitude) xlabel(frequency) ylabel(magnitude) subplot(222) plot(w,phaY) title(phase) xlabel(frequency) ylabel(phase)3(DFT compares to DTFT) N=10, 30, 50 b=1; a=1 0.9; L=100; NFFT=2nextpow2(L); N=10; h1=impz(b,a,N); H,w=freqz(b,a,NFFT,whole); y=fft(h1,NFFT); magY=abs(y); phaY=angle(y); subplot(221) plot(w,magY) hold on; plot(w,abs(H) hold off; title(magnitude) xlabel(frequency) ylabel(magnitude) subplot(222) plot(w,phaY) hold on; plot(w,angle(H) hold off; title(phase) xlabel(frequency) ylabel(phase)(b) a=-0.91（Z-P plane&impulse response&DTFT） b=1; a=1 -0.9; pul=1 zeros(1,59); subplot(221) zplane(b,a) title(zero-pole plane) subplot(222) h1=impz(b,a,60); stem(h1) title(impulse response) subplot(223) H,w=freqz(b,a,whole); plot(w,abs(H) title(|H(w)|) xlabel(w) subplot(224) plot(w,angle(H) title(angle H(w) xlabel(w)2(DFT) b=1; a=1 -0.9; L=100; NFFT=2nextpow2(L); N=10; h1=impz(b,a,N); H,w=freqz(b,a,NFFT); y=fft(h1,NFFT); magY=abs(y); phaY=angle(y); subplot(221) plot(w,magY) title(magnitude) xlabel(frequency) ylabel(magnitude) subplot(222) plot(w,phaY) title(phase) xlabel(frequency) ylabel(phase)3(DFT compares to DTFT) N=10, 30, 50 b=1; a=1 -0.9; L=100; NFFT=2nextpow2(L); N=10; h1=impz(b,a,N); H,w=freqz(b,a,NFFT,whole); y=fft(h1,NFFT); magY=abs(y); phaY=angle(y); subplot(221) plot(w,magY) hold on; plot(w,abs(H) hold off; title(magnitude) xlabel(frequency) ylabel(magnitude) subplot(222) plot(w,phaY) hold on; plot(w,angle(H) hold off; title(phase) xlabel(frequency) ylabel(phase)Problem 2:(a)1 (Z-P plane&impulse response&DTFT) b=1 -0.855; a=1 -1.71 0.9025; pul=1 zeros(1,59); subplot(221) zplane(b,a) title(zero-pole plane) subplot(222) h1=impz(b,a,60); stem(h1) title(impulse response) subplot(223) H,w=freqz(b,a,whole); plot(w,abs(H) title(|H(w)|) xlabel(w) subplot(224) plot(w,angle(H) title(angle H(w) xlabel(w)2 (DFT) b=1 -0.855; a=1 -1.71 0.9025; L=100; NFFT=2nextpow2(L); N=10; h1=impz(b,a,N); H,w=freqz(b,a,NFFT); y=fft(h1,NFFT); magY=abs(y); phaY=angle(y); subplot(221) plot(w,magY) title(magnitude) xlabel(frequency) ylabel(magnitude) subplot(222) plot(w,phaY) title(phase) xlabel(frequency) ylabel(phase)3 (DFT compares to DTFT) b=1 -0.855; a=1 -1.71 0.9025; L=100; NFFT=2nextpow2(L); N=10; h1=impz(b,a,N); H,w=freqz(b,a,NFFT,whole); y=fft(h1,NFFT); magY=abs(y); phaY=angle(y); subplot(221) plot(w,magY) hold on; plot(w,abs(H) hold off; title(magnitude) xlabel(frequency) ylabel(magnitude) subplot(222) plot(w,phaY) hold on; plot(w,angle(H) hold off; title(phase) xlabel(frequency) ylabel(phase)(b)1 (Z-P plane&impulse response&DTFT) b=1 -0.665; a=1 -1.33 0.9025; pul=1 zeros(1,59); subplot(221) zplane(b,a) title(zero-pole plane) subplot(222) h1=impz(b,a,60); stem(h1) title(impulse response) subplot(223) H,w=freqz(b,a,whole); plot(w,abs(H) title(|H(w)|) xlabel(w) subplot(224) plot(w,angle(H) title(angle H(w) xlabel(w)2 (DFT) b=1 -0.665; a=1 -1.33 0.9025; L=100; NFFT=2nextpow2(L); N=10; h1=impz(b,a,N); H,w=freqz(b,a,NFFT); y=fft(h1,NFFT); magY=abs(y); phaY=angle(y); subplot(221) plot(w,magY) title(magnitude) xlabel(frequency) ylabel(magnitude) subplot(222) plot(w,phaY) title(phase) xlabel(frequency) ylabel(phase)3 (DFT compares to DTFT) b=1 -0.665; a=1 -1.33 0.9025; L=100; NFFT=2nextpow2(L); N=50; h1=impz(b,a,N); H,w=freqz(b,a,NFFT,whole); y=fft(h1,NFFT); magY=abs(y); phaY=angle(y); subplot(221) plot(w,magY) hold on; plot(w,abs(H) hold off; title(magnitude) xlabel(frequency) ylabel(magnitude) subplot(222) plot(w,phaY) hold on; plot(w,angle(H) hold off; title(phase) xlabel(frequency) ylabel(phase)(c)1 (Z-P plane&impulse response&DTFT) b=1 -0.891; a=1 -1.782 0.9801; pul=1 zeros(1,59); subplot(221) zplane(b,a) title(zero-pole plane) subplot(222) h1=impz(b,a,60); stem(h1) title(impulse response) subplot(223) H,w=freqz(b,a,whole); plot(w,abs(H) title(|H(w)|) xlabel(w) subplot(224) plot(w,angle(H) title(angle H(w) xlabel(w)2 (DFT) b=1 -