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1、Name:CHEN YIFANV 20112121006Section:Laboratory Exercise 3DISCRETE-TIME SIGNALS: FREQUENCY-DOMAIN REPRESENTATIONS3.1 DISCRETE-TIME FOURIER TRANSFORMProject 3.1 DTFT ComputationA copy of Program P3_1 is given below:% Program P3_1% Evaluation of the DTFT clf;% Compute the frequency samples of the DTFTw
2、 = -4*pi:8*pi/511:4*pi;num = 2 1;den = 1 -0.6;h = freqz(num, den, w);% Plot the DTFTsubplot(2,1,1)plot(w/pi,real(h);gridtitle(Real part of H(ejomega)xlabel(omega /pi);ylabel(Amplitude);subplot(2,1,2)plot(w/pi,imag(h);gridtitle(Imaginary part of H(ejomega)xlabel(omega /pi);ylabel(Amplitude);pausesubp
3、lot(2,1,1)plot(w/pi,abs(h);gridtitle(Magnitude Spectrum |H(ejomega)|)xlabel(omega /pi);ylabel(Amplitude);subplot(2,1,2)plot(w/pi,angle(h);gridtitle(Phase Spectrum argH(ejomega)xlabel(omega /pi);Answers:Q3.1 The expression of the DTFT being evaluated in Program P3_1 is - jwjweeX6.012)(The function of
4、 the pause command is - causes M-files to stop and wait for you to press any key before continuing.Q3.2 The plots generated by running Program P3_1 are shown below:-4 -3 -2 -1 0 1 2 3 402468 Real part of H(ej) /Amplitude-4 -3 -2 -1 0 1 2 3 4-4-2024 Imaginary part of H(ej) /Amplitude-4 -3 -2 -1 0 1 2
5、 3 402468 Magnitude Spectrum |H(ej)| /Amplitude-4 -3 -2 -1 0 1 2 3 4-2-1012 Phase Spectrum argH(ej) /Phase, radiansThe DTFT is a period function of .Its period is - 2 piThe types of symmetries exhibited by the four plots are as follows: Real part of H(ejomega) is eve symmetries;Imaginary part of H(e
6、jomega) is ode symmetries;Magnitude Spectrum |H(ejomega)| is eve symmetries;Phase Spectrum argH(ejomega) is ode symmetries;Q3.3 The required modifications to Program P3_1 to evaluate the given DTFT of Q3.3 are given below:% Program Q3_3% Evaluation of the DTFTclf;% Compute the frequency samples of t
7、he DTFTw = 0:pi/511:pi;num = 0.7 -0.5 0.3 1;den = 1 0.3 -0.5 0.7;h = freqz(num, den, w);% Plot the DTFTsubplot(2,1,1)plot(w/pi,real(h);gridtitle(Real part of H(ejomega)xlabel(omega /pi);ylabel(Amplitude);subplot(2,1,2)plot(w/pi,imag(h);gridtitle(Imaginary part of H(ejomega)xlabel(omega /pi);ylabel(A
8、mplitude);pausesubplot(2,1,1)plot(w/pi,abs(h);gridtitle(Magnitude Spectrum |H(ejomega)|)xlabel(omega /pi);ylabel(Amplitude);subplot(2,1,2)plot(w/pi,angle(h);gridtitle(Phase Spectrum argH(ejomega)xlabel(omega /pi);ylabel(Phase, radians);The plots generated by running the modified Program P3_1 are sho
9、wn below:0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1-0.500.51 Real part of H(ej) /Amplitude0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-1-0.500.51 Imaginary part of H(ej) /Amplitude0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11111 Magnitude Spectrum |H(ej)| /Amplitude0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-4-202
10、4 Phase Spectrum argH(ej) /Phase, radiansThe DTFT is a perio function of . Its period is 2piThe jump in the phase spectrum is caused by - Change real component, so change phaseThe phase spectrum evaluated with the jump removed by the command unwrap is as given below:% Program Q3_3_1% Evaluation of t
11、he DTFTclf;% Compute the frequency samples of the DTFTw = 0:pi/511:pi;num = 0.7 -0.5 0.3 1;den = 1 0.3 -0.5 0.7;h = freqz(num, den, w);subplot(2,1,1)plot(w/pi,abs(h);gridtitle(Magnitude Spectrum |H(ejomega)|)xlabel(omega /pi);ylabel(Amplitude);subplot(2,1,2)p = angle(h(:); plot(w/pi,unwrap(p);gridti
12、tle(Phase Spectrum argH(ejomega)xlabel(omega /pi);ylabel(Phase, radians);0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 11111 Magnitude Spectrum |H(ej)| /Amplitude0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1-6-4-20 Phase Spectrum argH(ej) /Phase, radiansct 3.2 DTFT PropertiesAnswers:Q3.6 The modified Program P3_2
13、 created by adding appropriate comment statements, and adding program statements for labeling the two axes of each plot being generated by the program is given below:% Program P3_2% Time-Shifting Properties of DTFTclf;w = -pi:2*pi/255:pi; wo = 0.4*pi;D=10;num=1 2 3 4 5 6 7 8 9;h1 = freqz(num, 1, w);
14、h2 = freqz(zeros(1,D) num, 1, w);subplot(2,2,1)plot(w/pi,abs(h1);gridtitle(Magnitude Spectrum of Original Sequence)xlabel(omega /pi);ylabel(Amplitude);subplot(2,2,2)plot(w/pi,abs(h2);gridtitle(Magnitude Spectrum of Time-Shifted Sequence)xlabel(omega /pi);ylabel(Amplitude);subplot(2,2,3)plot(w/pi,ang
15、le(h1);gridtitle(Phase Spectrum of Original Sequence)xlabel(omega /pi);ylabel(Phase, radians);subplot(2,2,4)plot(w/pi,angle(h2);gridtitle(Phase Spectrum of Time-Shifted Sequence)xlabel(omega /pi);ylabel(Phase, radians);-1 -0.5 0 0.5 10204060Magnitude Spectrum of Original Sequence /Amplitude-1 -0.5 0 0.5 10204060Magnitude Spectrum of Time-Shifted Sequence /Amplitude-1 -0.5 0 0.5 1-4-2024Phase Spectrum of Original Sequence /Phase, radians-1 -0.5 0 0.5 1-4-2024Phase Spectrum of Time-Shifted Se
