数字信号处理实验报告材料2Word文档格式.docx

1、% Display the input and output signalsclf;subplot（2,2,1）;plot（n, s1）;axis（0, 100, -2, 2）;xlabel（Time index n ylabel（Amplitudetitle（Signal #1subplot（2,2,2）;plot（n, s2）;Signal #2subplot（2,2,3）;plot（n, x）;Input Signalsubplot（2,2,4）;plot（n, y）;Output Signal axis;Answers:Q2.1 The output sequence generate

2、d by running the above program for M = 2 with xn = s1n+s2n as the input is shown below. The component of the input xn suppressed by the discrete-time system simulated by this program is s2Q2.2 Program P2_1 is modified to simulate the LTI system yn = 0.5（xnxn1） and process the input xn = s1n+s2n resu

3、lting in the output sequence shown below:s3=cos（2*pi*0.05*（n-1）;s4= cos（2*pi*0.47*（n-1）;z=s3+s4;y = 0.5*（x-z）; The effect of changing the LTI system on the input is - Project 2.2 （Optional） A Simple Nonlinear Discrete-Time System A copy of Program P2_2 is given below: % Program P2_2% Generate a sinu

4、soidal input signal200;x = cos（2*pi*0.05*n）;% Compute the output signalx1 = x 0 0; % x1n = xn+1 x2 = 0 x 0; % x2n = xnx3 = 0 0 x; % x3n = xn-1y = x2.*x2-x1.*x3;y = y（2:202）;% Plot the input and output signalssubplot（2,1,1）plot（n, x）ylabel（）subplot（2,1,2）plot（n,y）Output signalQ2.5 The sinusoidal sign

5、als with the following frequencies as the input signals were used to generate the output signals: The output signals generated for each of the above input signals are displayed below: The output signals depend on the frequencies of the input signal according to the following rules: This observation

6、can be explained mathematically as follows:Project 2.3 Linear and Nonlinear Systems A copy of Program P2_3 is given below: % Program P2_3% Generate the input sequences40;a = 2;b = -3;x1 = cos（2*pi*0.1*n）;x2 = cos（2*pi*0.4*n）;x = a*x1 + b*x2;num = 2.2403 2.4908 2.2403;den = 1 -0.4 0.75;ic = 0 0; % Se

7、t zero initial conditionsy1 = filter（num,den,x1,ic）; % Compute the output y1ny2 = filter（num,den,x2,ic）; % Compute the output y2ny = filter（num,den,x,ic）; % Compute the output ynyt = a*y1 + b*y2;d = y - yt; % Compute the difference output dn% Plot the outputs and the difference signalsubplot（3,1,1）s

8、tem（n,y）;Output Due to Weighted Input: a cdot x_1n + b cdot x_2nsubplot（3,1,2）stem（n,yt）;Weighted Output: a cdot y_1n + b cdot y_2nsubplot（3,1,3）stem（n,d）;Difference SignalQ2.7 The outputs yn, obtained with weighted input, and ytn, obtained by combining the two outputs y1n and y2n with the same weig

9、hts, are shown below along with the difference between the two signals:The two sequences are same ;we can regard 10（-15） as 0 The system is a liner systemQ2.9 Program 2_3 was run with the following non-zero initial conditions - ic = 2 2; The plots generated are shown below - Based on these plots we

10、can conclude that the system with nonzero initial conditions is as same as the zero initial condition with the time goneProject 2.4 Time-invariant and Time-varying Systems A copy of Program P2_4 is given below: % Program P2_4 D = 10;a = 3.0;b = -2;x = a*cos（2*pi*0.1*n） + b*cos（2*pi*0.4*n）;xd = zeros

11、（1,D） x; % Set initial conditions% Compute the output yn% Compute the output ydnyd = filter（num,den,xd,ic）;% Compute the difference output dnd = y - yd（1+D:41+D）;% Plot the outputsOutput yn grid;stem（n,yd（1:41）;title（Output due to Delayed Input xn ?, num2str（D）,）; Answers:Q2.12 The output sequences

12、yn and ydn-10 generated by running Program P2_4 are shown below - These two sequences are related as follows same, the output dont change with the time The system is - Time invariant systemQ2.15 The output sequences yn and ydn-10 generated by running Program P2_4 for non-zero initial conditions are

13、shown below - ic = 5 2;These two sequences are related as follows just as the sequences above The system is not related to the initial conditions2.2 LINEAR TIME-INVARIANT DISCRETE-TIME SYSTEMSProject 2.5 Computation of Impulse Responses of LTI Systems A copy of Program P2_5 is shown below: % Program

14、 P2_5% Compute the impulse response yN = 40;y = impz（num,den,N）;% Plot the impulse responsestem（y）;Impulse ResponseQ2.19 The first 41 samples of the impulse response of the discrete-time system of Project 2.3 generated by running Program P2_5 is given below:Project 2.6 Cascade of LTI Systems A copy

15、of Program P2_6 is given below: % Program P2_6% Cascade Realizationx = 1 zeros（1,40）; % Generate the input% Coefficients of 4th order systemden = 1 1.6 2.28 1.325 0.68;num = 0.06 -0.19 0.27 -0.26 0.12;% Compute the output of 4th order systemy = filter（num,den,x）;% Coefficients of the two 2nd order s

16、ystemsnum1 = 0.3 -0.2 0.4;den1 = 1 0.9 0.8;num2 = 0.2 -0.5 0.3;den2 = 1 0.7 0.85;% Output y1n of the first stage in the cascadey1 = filter（num1,den1,x）;% Output y2n of the second stage in the cascadey2 = filter（num2,den2,y1）;% Difference between yn and y2nd = y - y2;% Plot output and difference sign

17、alssubplot（3,1,1）;Output of 4th order Realizationsubplot（3,1,2）;stem（n,y2）Output of Cascade Realizationsubplot（3,1,3）;stem（n,d）Q2.23 The output sequences yn, y2n, and the difference signal dn generated by running Program P2_6 are indicated below: The relation between yn and y2n is yn is the Convolut

18、ion of y2n and y1nThe 4th order system can do the same job as the cascade systemQ2.24 The sequences generated by running Program P2_6 with the input changed to a sinusoidal sequence are as follows: x = sin（2*pi*0.05*n）; The relation between yn and y2n in this case is same as the relation aboveProjec

19、t 2.7 Convolution A copy of Program P2_7 is reproduced below: % Program P2_7h = 3 2 1 -2 1 0 -4 0 3; % impulse responsex = 1 -2 3 -4 3 2 1; % input sequencey = conv（h,x）;14;subplot（2,1,1）;Output Obtained by Convolutionx1 = x zeros（1,8）;y1 = filter（h,1,x1）;subplot（2,1,2）;stem（n,y1）;Output Generated b

20、y FilteringQ2.28 The sequences yn and y1n generated by running Program P2_7 are shown below:The difference between yn and y1n is - same The reason for using x1n as the input, obtained by zero-padding xn, for generating y1n is the length of x is 7,but the length of the Convolution is 14,and n=14,we n

21、eed the length of filter to be 14Project 2.8 Stability of LTI Systems A copy of Program P2_8 is given below: % Program P2_8% Stability test based on the sum of the absolute % values of the impulse response samplesnum = 1 -0.8; den = 1 1.5 0.9;N = 200;h = impz（num,den,N+1）;parsum = 0;for k = 1:N+1; p

22、arsum = parsum + abs（h（k）; if abs（h（k） 10（-6）, break, endendN;stem（n,h）% Print the value of abs（h（k） disp（Value =disp（abs（h（k）;Q2.32 The discrete-time system of Program P2_8 is - h,t = impz（hd） computes the instantaneous impulse response of the discrete-time filter hd choosing the number of samples

23、for you, and returns the response in column vector h and a vector of times or sample intervals in t where （t = 0 1 2.）. impz returns a matrix h if hd is a vector. Each column of the matrix corresponds to one filter in the vector. When hd is a vector of discrete-time filters, impz returns the matrix

24、h. Each column of h corresponds to one filter in the vector hd. impz（hd） uses FVTool to plot the impulse response of the discrete-time filter hd. If hd is a vector of filters, impz plots the response and for each filter in the vector. The impulse response generated by running Program P2_8 is shown below:The value of |h（K）| here is - 1.6761e-005 From this value