MATLAB 编程 Zero-pole plane, impulse response,impulse response of DTFT and DFT
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Projects 1: Part A
Problem 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) =2
2101
0)cos(21)cos(1---+--z r z w r z w r Where (a) ω0=π/8 and r=0.95;
(b) ω0=π/4 and r=0.95; (c ) ω0=π/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 23
When N=30: in figure 24.
When N=50: in figure 25.
Figure 25.
Problem 1:
(a) a=0.9
1（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=2^nextpow2(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)