数字信号处理实验五.doc

Name:段宏坤Section:20121060177Laboratory Exercise 5DIGITAL PROCESSING OF CONTINUOUS-TIME SIGNALS5.1THE SAMPLING PROCESS IN THE TIME-DOMAINProject 5.1Sampling of a Sinusoidal SignalA copy of Program P5_1 is given below:%程序P5.1%在时间域中抽样过程的说明clf;t=0:0.0005:1;f=13;xa=cos(2*pi*f*t);subplot(2,1,1)plot(t,xa);gridxlabel(时间，msec);ylabel(振幅);title(连续时间信号x_a(t);axis(0 1 -1.2 1.2)subplot(2,1,2);T=0.1;n=0:T:1;xs=cos(2*pi*f*n);k=0:length(n)-1;stem(k,xs);gridxlabel(时间序号n);ylabel(振幅);title(离散时间信号xn);axis(0 (length(n)-1) -1.2 1.2)Answers:Q5.1The plots of the continuous-time signal and its sampled version generated by running Program P5_1 are shown below:Q5.2The frequency of the sinusoidal signal in Hz is - 13HzThe sampling period in seconds is -0.1sQ5.4The plots of the continuous-time signal and its sampled version generated by running Program P5_1 for the following four values of the sampling period are shown below: T=0.01：T=0.05：T=0.2：T=0.5：Based on these results we make the following observations - 由结果可以看出随着抽样周期变小，即抽样间隔变密，抽样后的结果越接近原始正弦信号，抽样周期越大即抽样间隔越大，抽样结果失真严重。Project 5.2Aliasing Effect in the Time-DomainA copy of Program P5_2 is given below:%程序P5.2%时域中混叠效果的说明clf;T=0.1;f=13;n=(0:T:1);xs=cos(2*pi*f*n);t=linspace(-0.5,1.5,500);ya=sinc(1/T)*t(:,ones(size(n)-(1/T)*n(:,ones(size(t)*xs;plot(n,xs,o,t,ya);grid;xlabel(时间，msec);ylabel(振幅);title(重构的连续时间信号y_a(t);axis(0 1 -1.2 1.2)Answers:Q5.6The plots of the discrete-time signal and its continuous-time equivalent obtained by running Program P5_2 are shown below:Q5.7The range of t in the Program is -（-0.5,1.5）The value of the time increment is -The range of t in the plot is -（0,1） The plot generated by running Program P5_2 again with the range of t changed so as to display the full range of ya(t) is shown below:Based on these results we make the following observations - 将图中t的范围改成（-0.5,1.5）。改变后产生的曲线在时间轴（0,1）上逼近重构的连续时间信 ya(t),在这范围外差别大。5.2EFFECT OF SAMPLING IN THE FREQUENCY-DOMAIN Project 5.3Aliasing Effect in the Frequency-DomainA copy of Program P5_3 is given below:%程序P5.3%频域中混叠效果clf;t=0:0.005:10;xa=2*t.*exp(-t);subplot(2,2,1)plot(t,xa);gridxlabel(时间，msec);ylabel(振幅);title(连续时间信号x_a(t);subplot(2,2,2);wa=0:10/511:10;ha=freqs(2,1 2 1,wa);plot(wa/(2*pi),abs(ha);grid;xlabel(频率，kHZ);ylabel(振幅);title(|X_a(jOmega)|);axis(0 5/pi 0 2);subplot(2,2,3)T=1;n=0:T:10;xs=2*n.*exp(-n);k=0:length(n)-1;stem(k,xs);grid;xlabel(时间序号n);ylabel(振幅);title(离散时间信号xn);subplot(2,2,4)wd=0:pi/225:pi;hd=freqs(xs,1,wd);plot(wd/(T*pi),T*abs(hd);grid;xlabel(频率，kHZ);ylabel(振幅);title(|X(ejOmega|);axis(0 1/T 0 2);Answers:Q5.9The continuous-time function xa(t) in Program P5_3 is -是能量信号衰减信号。 The CTFT of xa(t) is being computed by -Q5.10 The plots generated by running Program P5_3 are shown below: Based on these results we make the following observations - 有明显的混叠现象，比较和在0.5的值可知在f=0.5kHz处发生混叠现象。5.3DESIGN OF ANALOG LOWPASS FILTERSProject 5.4Design of Analog Lowpass FiltersA copy of Program P5_4 is given below:Answers:Q5.13The passband ripple Rp in dB is -The minimum stopband attenuation Rs in dB is - The passband edge frequency in Hz is - The stopband edge frequency in Hz is - Q5.14The gain response obtained by running Program P5_4 is shown below:Based on this plot we conclude that the filter designed _ the given specifications. The filter order N is -The 3-dB cutoff frequency in Hz of the filter is - Q5.15 The required modifications to Program P5_4 to design a Type 1 Chebyshev lowpass filter meeting the same specifications are given below:The gain response obtained by running the modified Program P5_4 is shown below:Based on this plot we conclude that the filter designed _ the given specifications. The filter order N is -The passband edge frequency in Hz of the filter is - Q5.16 The required modifications to Program P5_4 to design a Type 2 Chebyshev lowpass filter meeting the same specifications are given below:The gain response obtained by running the modified Program P5_4 is shown below:Based on this plot we conclude that the filter designed _ the given specifications. The filter order N is -The stopband edge frequency in Hz of the filter is - Q5.17 The required modifications to Program P5_4 to design an elliptic lowpass filter meeting the same specifications are given below:The gain response obtained by running the modified Program P5_4 is shown below:Based on this plot we conclude that the filter designed _ the given specifications. The filter order N is -The passband edge frequency in Hz of the filter is - 5.4A/D AND D/A CONVERSIONSProject 5.5Binary Equivalent of a Decimal NumberAnswers:Q5.18The function of the operator = is -Q5.19The binary equivalents in sign-magnitude form of the decimal fractions are:(a) (b) (c) (d) Project 5.6Decimal Equivalent of a Binary NumberAnswer:Q5.20The decimal equivalents of the binary fractions along with the errors in conversion are as follows:(a)(b)(c)(d)Project 5.7Binary Number Representation SchemesAnswers:Q5.21The function of the operator = is -Q5.22The ones-complement representations of the binary numbers developed in Question Q5.19 are as follows:(a)(b)(c)(d)Q5.23The function of the operator | is The function of the operator & is Q5.24The twos-complement representations of the binary numbers developed in Question Q5.19 are as follows:(a)(b)(c)(d)Project 5.8D/A Converter Droop Compen