武汉大学数字信号实验三

姓名:全权 学号：2013302530120 班级：信安四班 日期：5月8日实验3离散时间系统-频域分析实验内容：3.1 DISCRETE-TIME FOURIER TRANSFORM(离散时间傅立叶变换)Project 3.1 DTFT ComputationA copy of Program P3_1 is given below :% Program P3_1% Evaluation of the DTFTclf;% Compute the frequency samples of the DTFTw = -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(e^{j\omega})')xlabel('\omega /\pi');ylabel('Amplitude');subplot(2,1,2)plot(w/pi,imag(h));gridtitle('Imaginary part of H(e^{j\omega})')xlabel('\omega /\pi');ylabel('Amplitude');pausesubplot(2,1,1)plot(w/pi,abs(h));gridtitle('Magnitude Spectrum |H(e^{j\omega})|')xlabel('\omega /\pi');ylabel('Amplitude');subplot(2,1,2)plot(w/pi,angle(h));gridtitle('Phase Spectrum arg[H(e^{j\omega})]')xlabel('\omega /\pi');ylabel('Phase in radians');< Insert program code here. Copy from m-file(s) and paste. >Answers :Q3.1 The expression of the DTFT being evaluated in ProgramP3_1 is - 112()()10.6j j j z e z e z H e H z z ωωω--==+==-The function of the pause command is - 暂停程序执行Q3.2 The plots generated by running Program P3_1 are shown below :< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. >The DTFT is a 周期性 function of ω.Its period （周期） is -____2π______ The types of symmetries(对称性) exhibited by the four plots are as follows :实部周期为2π且对称，虚部周期为2π且为奇函数，幅度为2π且为偶函数，相位为2π且为奇函数（指导说明：P3_1原始程序中的参数确定的系统函数为：112()()10.6j j j z e z e z H e H z z ωωω--==+==-，通过调整变量num ，den ，w 观察频率响应的变化）Q3.3 The required modifications to Program P3_1 to evaluate the given DTFT of Q3.3 aregiven below :N=512;num = [0.7 -0.5 0.3 1];den = [1 0.3 -0.5 0.7];[h,w] = freqz(num,den,N);% Plot the DTFT subplot(2,1,1)plot(w/pi,real(h));gridtitle('Real part of H(e^{j\omega})');xlabel('\omega/\pi');ylabel('Amplitude');subplot(2,1,2)plot(w/pi,imag(h));gridtitle('Imaginary part of H(e^{j\omega})');xlabel('\omega/\pi');ylabel('Amplitude');pausesubplot(2,1,1)plot(w/pi,abs(h));gridtitle('Magnitude Spectrum |H(e^{j\omega})|');xlabel('\omega/\pi');ylabel('Amplitude');subplot(2,1,2)plot(w/pi,angle(h));gridtitle('Phase Spectrum arg[H(e^{j\omega})]');xlabel('\omega /\pi'); ylabel('Phase in radians');< Insert program code here. Copy from m-file(s) and paste. >The plots generated by running the modified Program P3_1 are shown below:< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. >The DTFT is a ____周期性_______ function of .Its period is - ____2π_______The jump in the phase（相位） spectrum is caused by - ____arctan反函数计算_______ The phase spectrum evaluated with the jump removed by the command unwrap is as given below:< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. > Q3.4The required modifications to Program P3_1 to evaluate the given DTFT of Q3.4 are given below:% Program P3_1D% Evaluation of the DTFTclf;% Compute the frequency samples of the DTFTw=-4*pi:8*pi/511:4*pi;num=[1 3 5 7 9 11 13 15 17]; den = 1;h=freqz(num,den,w);% Plot the DTFTsubplot(2,1,1)plot(w/pi,real(h));gridtitle('Real part of H(e^{j\omega})')xlabel('\omega /\pi');ylabel('Amplitude');subplot(2,1,2)plot(w/pi,imag(h));gridtitle('Imaginary part of H(e^{j\omega})')xlabel('\omega /\pi');ylabel('Amplitude');pausesubplot(2,1,1)plot(w/pi,abs(h));gridtitle('Magnitude Spectrum |H(e^{j\omega})|')xlabel('\omega /\pi');ylabel('Amplitude');subplot(2,1,2)plot(w/pi,angle(h));gridtitle('Phase Spectrum arg[H(e^{j\omega})]')xlabel('\omega /\pi');ylabel('Phase in radians');< Insert program code here. Copy from m-file(s) and paste. > The plots generated by running the modified Program P3_1 are shown below:< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. > The DTFT is a 周期性function of .Its period is -_____2π______The jump in the phase spectrum is caused by–______angle角度返回arctan函数主值_____ Q3.5The required modifications to Program P3_1 to plot the phase in degrees are indicated below:% plot phase in degrees subplot(2,1,2)plot(w/pi,180*angle(h)/pi);gridtitle('Phase Spectrum arg[H(e^{j\omega})]')xlabel('\omega /\pi');ylabel('Phase in degrees');< Insert program code here. Copy from m-file(s) and paste. >Project 3.2 DTFT PropertiesAnswers:Q3.6 The modified Program P3_2 created by adding appropriate comment statements(添加适当的注释语句), and adding program statements for labeling the two axes(添加标注两个坐标轴的程序语句) of each plot being generated by the program is given below:% Program P3_2B% Time-Shifting Properties of DTFTclf;w=-pi:2*pi/255:pi;% freqency vector for evaluating DTFTD=10;% Amount of time shift in samplesnum=[1 2 3 4 5 6 7 8 9];% h1 is the DTFT of original sequence% h2 is the DTFT of the time shifted sequenceh1=freqz(num,1,w);h2=freqz([zeros(1,D) num],1,w);subplot(2,2,1)% plot the DTFT magnitude of the original sequenceplot(w/pi,abs(h1));gridtitle('Magnitude Spectrum of Original Sequence','FontSize',8)xlabel('\omega /\pi');ylabel('Amplitude');% plot the DTFT magnitude of the shifted sequencesubplot(2,2,2)plot(w/pi,abs(h2));gridtitle('Magnitude Spectrum of Time-Shifted Sequence','FontSize',8)xlabel('\omega /\pi');ylabel('Amplitude');% plot the DTFT phase of the original sequencesubplot(2,2,3)plot(w/pi,angle(h1));gridtitle('Phase Spectrum of Original Sequence','FontSize',8)xlabel('\omega /\pi');ylabel('Phase in radians');% plot the DTFT phase of the shifted sequencesubplot(2,2,4)plot(w/pi,angle(h2));gridtitle('Phase Spectrum of Time-Shifted Sequence','FontSize',8)xlabel('\omega /\pi');ylabel('Phase in radians');< Insert program code here. Copy from m-file(s) and paste. >The parameter controlling the amount of time-shift(时移) is– D _Q3.7The plots generated by running the modified program are given below:< Insert MATLAB figure(s) here. Copy from figure window(s) and paste. > From these plots we make the following observations:_时间变化不影响幅度谱。