实验四(华电版)

1、实验四 离散系统分析一、实验目的 深刻理解离散时间系统的系统函数在分析离散系统的时域特性、频域特性以及稳定性中的重要作用及意义，熟练掌握利用MATLAB分析离散系统的时域响应、频响特性和零极点的方法。掌握利用DTFT和DFT确定系统特性的原理和方法。 二、 实验原理 MATLAB提供了许多可用于分析线性时不变连续系统的函数，主要包含有系统函数、系统时域响应、系统频域响应等分析函数。例题：离散系统的单位脉冲响应N=40; a=1,0.4,-0.12;b=1,2; y=impz(b,a,N); stem(y) xlabel('k');title('hk')N=100

2、; b=1,2; a=1,0.4,-0.12; x=ones(1,N); y=filter(b,a,x)y = Columns 1 through 12 1.0000 2.6000 2.0800 2.4800 2.2576 2.3946 2.3131 2.3621 2.3327 2.3504 2.3398 2.3461 Columns 13 through 24 2.3423 2.3446 2.3432 2.3441 2.3436 2.3439 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 Columns 25 through 36 2.3437 2.34

3、38 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 Columns 37 through 48 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 Columns 49 through 60 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 Columns 61 thro

4、ugh 72 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3438 2.3438 Columns 73 through 84 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 Columns 85 through 96 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.34

5、38 Columns 97 through 100 2.3438 2.3438 2.3438 2.3438>> N=100; b=1,2; a=1,0.4,-0.12; x=ones(1,N); zi=filtic(b,a,1,2); y=filter(b,a,x,zi)y = Columns 1 through 12 0.8400 2.7840 1.9872 2.5392 2.2228 2.4156 2.3005 2.3697 2.3282 2.3531 2.3381 2.3471 Columns 13 through 24 2.3417 2.3450 2.3430 2.3442

6、 2.3435 2.3439 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 Columns 25 through 36 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 Columns 37 through 48 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 Columns 49 through 60 2.3437 2.

7、3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 Columns 61 through 72 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3437 2.3438 2.3438 2.3438 Columns 73 through 84 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 Columns 85 th

8、rough 96 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 2.3438 Columns 97 through 100 2.3438 2.3438 2.3438 2.3438>实验内容：>计算该系统函数的零极点，并画出系统函数零极点分布图。b=1,2,0; a=1,0.4,-0.12;z=roots(b)p=roots(a)zplane(b,a)分析系统的幅频特性。b=1,1;a=1,-1,0.5;H,w=freqz(b,a);plot(w,abs(H)xlabel(&#

9、39;Frequency(rad)');ylabel('Magnitude');title('Magnitude response');三、 实验内容1.已知某LTI系统的差分方程为：（1）初始状态 ， 输入 计算系统的完全响应。（2）当以下三个信号分别通过系统时，分别计算离散系统的零状态响应：（3）该系统具有什么特性？ N=100; b=0.0675,0.1349,0.0675; a=1,-1.143,0.412; x=ones(1,N); zi=filtic(b,a,1,2);y=filter(b,a,x,zi)y = Columns 1 throu

10、gh 12 0.3865 0.2322 0.3760 0.6041 0.8054 0.9416 1.0143 1.0413 1.0422 1.0322 1.0202 1.0108 Columns 13 through 24 1.0049 1.0020 1.0012 1.0015 1.0021 1.0027 1.0031 1.0033 1.0034 1.0035 1.0034 1.0034 Columns 25 through 36 1.0034 1.0034 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.003

11、3 Columns 37 through 48 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 Columns 49 through 60 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 Columns 61 through 72 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1

12、.0033 1.0033 1.0033 Columns 73 through 84 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 Columns 85 through 96 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 1.0033 Columns 97 through 100 1.0033 1.0033 1.0033 1.0033 N=40; b=0.0675,0.

13、1349,0.0675; a=1,-1.143,0.412; k=0:N-1 x=cos(pi*k/10);y=filter(b,a,x)y = Columns 1 through 12 0.0675 0.2762 0.5383 0.7145 0.7497 0.6438 0.4271 0.1415 -0.1690 -0.4644 -0.7116 -0.8854 Columns 13 through 24 -0.9692 -0.9560 -0.8482 -0.6569 -0.4014 -0.1068 0.1981 0.4834 0.7213 0.8886 0.9689 0.9544 Column

14、s 25 through 36 0.8464 0.6556 0.4006 0.1065 -0.1981 -0.4833 -0.7212 -0.8885 -0.9688 -0.9543 -0.8464 -0.6556 Columns 37 through 40 -0.4006 -0.1065 0.1981 0.4833 N=40; b=0.0675,0.1349,0.0675; a=1,-1.143,0.412; k=0:N-1 x=cos(pi*k/5);y=filter(b,a,x)stem(y)y = Columns 1 through 12 0.0675 0.2667 0.4745 0.

15、5079 0.3096 -0.0529 -0.4321 -0.6696 -0.6628 -0.4062 0.0062 0.4186 Columns 13 through 24 0.6734 0.6727 0.4160 0.0008 -0.4146 -0.6717 -0.6724 -0.4163 -0.0014 0.4141 0.6714 0.6722 Columns 25 through 36 0.4163 0.0014 -0.4141 -0.6713 -0.6722 -0.4163 -0.0014 0.4141 0.6713 0.6722 0.4163 0.0014 Columns 37 t

16、hrough 40 -0.4141 -0.6713 -0.6722 -0.4163 N=40; b=0.0675,0.1349,0.0675; a=1,-1.143,0.412; k=0:N-1 x=cos(7*pi*k/10);y=filter(b,a,x)stem(y)y = Columns 1 through 12 0.0675 0.1724 0.1366 0.0679 0.0742 0.0119 -0.0170 0.0206 -0.0223 -0.0168 0.0227 -0.0227 Columns 13 through 24 -0.0027 0.0235 -0.0249 0.006

17、8 0.0180 -0.0271 0.0144 0.0105 -0.0266 0.0208 0.0021 -0.0233 Columns 25 through 36 0.0253 -0.0064 -0.0178 0.0273 -0.0143 -0.0104 0.0266 -0.0208 -0.0021 0.0233 -0.0253 0.0064 Columns 37 through 40 0.0178 -0.0273 0.0143 0.0104题二： N=40; b=0.03571,0.1428,0.2143,0.1428,0.03571; a=1,-1.035,0.8264,-0.2605,

18、0.04033; y=impz(b,a,N)stem(y)y = 0.0357 0.1798 0.3708 0.3874 0.1756 -0.0491 -0.1099 -0.0431 0.0264 0.0362 0.0089 -0.0121 -0.0115 -0.0011 0.0049 0.0034 -0.0003 -0.0018 -0.0010 0.0003 0.0006 0.0002 -0.0002 -0.0002 -0.0000 0.0001 0.0001 0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 -0.0000 -0.000

19、0 0.0000 0.0000 0.0000 -0.0000 N=40; b=0.03571,0.1428,0.2143,0.1428,0.03571; a=1,-1.035,0.8264,-0.2605,0.04033; k=0:N-1 x=1+cos(pi*k/4)+cos(pi*k/2);y=filter(b,a,x)stem(y)y = Columns 1 through 12 0.1071 0.6002 1.4194 1.8056 1.2763 0.4514 0.1235 0.2914 0.6941 1.3572 2.0325 2.0167 Columns 13 through 24

20、 1.1617 0.2874 0.0788 0.3423 0.7456 1.3634 2.0114 2.0012 1.1625 0.2954 0.0832 0.3411 Columns 25 through 36 0.7428 1.3623 2.0121 2.0021 1.1627 0.2951 0.0829 0.3411 0.7429 1.3624 2.0121 2.0021 Columns 37 through 40 1.1627 0.2951 0.0829 0.3411题三： N=40; k=0:N-1 x=0.5.k; y=0.25*(0.5).k+(0.25).k; X = fft(

21、x,N); Y = fft(y,N); H = Y./X ; h = ifft(H,N) stem(h)h = Columns 1 through 12 1.2500 -0.2500 -0.0625 -0.0156 -0.0039 -0.0010 -0.0002 -0.0001 -0.0000 -0.0000 -0.0000 -0.0000 Columns 13 through 24 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 -0.0000 Columns 25

22、 through 36 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 Columns 37 through 40 -0.0000 0.0000 0.0000 0.0000 N=40; k=0:N-1 x=0.25.k; y=(0.25).k-(0.25).(k-1); X = fft(x,N); Y = fft(y,N); H = Y./X ; h = ifft(H,N) stem(h)h = Columns 1 through 12 -3.0000 -0

23、.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 0.0000 Columns 13 through 24 0.0000 -0.0000 0.0000 -0.0000 -0.0000 -0.0000 -0.0000 0.0000 0 0.0000 -0.0000 -0.0000 Columns 25 through 36 -0.0000 0.0000 -0.0000 -0.0000 0.0000 0.0000 0.0000 -0.0000 0.0000 -0.0000 0.0000 -0.0000

24、Columns 37 through 40 -0.0000 -0.0000 -0.0000 -0.0000题四：x=2,0.8333,0.3611,0.162,0.0748,0.0354,0.017,0.0083,0.0041,0.002,0.001,0.0005,0.0002,0.0001,0.0001;y=0.0056,-0.0259,0.073,-0.1593,0.297,-0.4974,0.7711,-1.1267,1.5702,-2.1037,2.724,-3.4207,4.174,-4.9528,5.7117,-6.3889,6.9034,-7.1528,7.012,-6.3322

25、,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533,-29.6298,41.4666,-55.2433,70.7979,-87.7810;subplot(2,1,1);stem(x);subplot(2,1,2);stem(y);x=2,0.8333,0.3611,0.162,0.0748,0.0354,0.017,0.0083,0.0041,0.002,0.001,0.0005,0.0002,0.0001,0.0001;y=0.0056,-0.0259,0.073,-0.1593,0.297,-0.4974,0.7711,-1.1267,1.5702

26、,-2.1037,2.724,-3.4207,4.174,-4.9528,5.7117,-6.3889,6.9034,-7.1528,7.012,-6.3322,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533,-29.6298,41.4666,-55.2433,70.7979,-87.7810;X=fft(x,256);Y=fft(y,256);H=Y./X;H0=abs(H);plot(H0);x=2,0.8333,0.3611,0.162,0.0748,0.0354,0.017,0.0083,0.0041,0.002,0.001,0.0005,0

27、.0002,0.0001,0.0001;y=0.0056,-0.0259,0.073,-0.1593,0.297,-0.4974,0.7711,-1.1267,1.5702,-2.1037,2.724,-3.4207,4.174,-4.9528,5.7117,-6.3889,6.9034,-7.1528,7.012,-6.3322,4.9416,-2.648,-0.7564,5.4872,-11.7557,19.7533,-29.6298,41.4666,-55.2433,70.7979,-87.7810;X=fft(x,256);Y=fft(y,256);H=Y./X;h=ifft(H);plot(h);题五：a=1,-3.594,5.17,-3.494,0.945;b=0.6877,-2.509,3.664,-2.509,0.6877;z=roots(b);p=roots(a);subplot(3,1,1);zplane(b,a);H,w=freqz(b,a);title('零极点分布图')subplot(3,1,2);plot(w,abs(H);xlabel('w');ylabel('H0');title('幅频特性');subplot(3,1,3);