数字信号处理实验二.docx

1、数字信号处理实验二 实验二 Q2-1n = 0:100;s1 = cos(2*pi*0.05*n); s2 = cos(2*pi*0.47*n);x = s1+s2;M = input(滤波器所需长度=);num = ones(1,M);y = filter(num,1,x)/M;clf;subplot(2,2,1);plot(n, s1);axis(0, 100, -2, 2);xlabel(时间序号n); ylabel(振幅);title(信号#1);subplot(2,2,2);plot(n, s2);axis(0, 100, -2, 2);xlabel(时间序号n ); ylabel(

2、振幅);title(信号#2);subplot(2,2,3);plot(n, x);axis(0, 100, -2, 2);xlabel(时间序号n ); ylabel(振幅);title(输入信号);subplot(2,2,4);plot(n, y);axis(0, 100, -2, 2);xlabel(时间序号n ); ylabel(振幅);title(输入信号); axis;输入的频率分量被离散时间系统抑制Q2-2线性时不变系统发生改变后，输入x的频率会发生改变。Q2-5clf;n = 0:200;x = cos(2*pi*0.05*n);x1 = x 0 0; x2 = 0 x 0;

3、x3 = 0 0 x; y = x2.*x2-x1.*x3;y = y(2:202);subplot(2,1,1)plot(n, x)xlabel(时间序号n);ylabel(振幅);title(输入信号)subplot(2,1,2)plot(n,y)xlabel(时间序号n n);ylabel(振幅);title(输出信号);当输入信号为cos(2*pi*0.1*n)时；当输入信号为cos(2*pi*0.01*n)时；当输入信号频率大于一定值时，输出信号的最低幅值为零。Q2-7clf;n = 0:40;a = 2;b = -3;x1 = cos(2*pi*0.1*n);x2 = cos(2*

4、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; y1 = filter(num,den,x1,ic); y2 = filter(num,den,x2,ic); y = filter(num,den,x,ic);yt = a*y1 + b*y2; d = y - yt; subplot(3,1,1)stem(n,y);ylabel(振幅);title(加权输入: a cdot x_1n + b cdot x_2n);subplot(3,1,2)stem(n,yt);ylabel(振幅

5、);title(加权输出: a cdot y_1n + b cdot y_2n);subplot(3,1,3)stem(n,d);xlabel(时间序号n);ylabel(振幅);title(差信号);两个序列并不相等，该系统不是线性系统。Q2-9初始条件设为ic = 3 10; 系统在一定n之后趋于线性系统。Q2-12clf;n = 0:40; D = 10;a = 3.0;b = -2;x = a*cos(2*pi*0.1*n) + b*cos(2*pi*0.4*n);xd = zeros(1,D) x;num = 2.2403 2.4908 2.2403;den = 1 -0.4 0.7

6、5;ic = 0 0;y = filter(num,den,x,ic);yd = filter(num,den,xd,ic);d = y - yd(1+D:41+D);subplot(3,1,1)stem(n,y);ylabel(振幅); title(输出yn); grid;subplot(3,1,2)stem(n,yd(1:41);ylabel(振幅);title(由于延时输入xn, num2str(D),); grid;subplot(3,1,3)stem(n,d);xlabel(时间序号n); ylabel(振幅);title(差值信号); grid;这两个序列是延时的关系，该系统是时不

7、变系统。Q2-15初始条件设为ic = 3 10;该系统不是时不变系统。Q2-19 clf;N = 40;num = 2.2403 2.4908 2.2403;den = 1 -0.4 0.75;y = impz(num,den,N);stem(y);xlabel(时间序号n); ylabel(振幅);title(冲激响应); grid;Q2-23clf;x = 1 zeros(1,40); n = 0:40;den = 1 1.6 2.28 1.325 0.68;num = 0.06 -0.19 0.27 -0.26 0.12;y = filter(num,den,x);num1 = 0.3

8、 -0.2 0.4;den1 = 1 0.9 0.8;num2 = 0.2 -0.5 0.3;den2 = 1 0.7 0.85;y1 = filter(num1,den1,x);y2 = filter(num2,den2,y1);d = y - y2;subplot(3,1,1);stem(n,y);ylabel(振幅);title(四阶实现的输出); grid;subplot(3,1,2);stem(n,y2)ylabel(振幅);title(级联实现的输出); grid;subplot(3,1,3);stem(n,d)xlabel(时间序号m);ylabel(振幅);title(差值信号

9、); grid;Yn和y2n是不相等的。Q2-25Ic1：2 2 5 4 Ic2：0 2 Ic3：3 5 Q2-28clf;h = 3 2 1 -2 1 0 -4 0 3; x = 1 -2 3 -4 3 2 1; y = conv(h,x);n = 0:14;subplot(2,1,1);stem(n,y);xlabel(时间序号n); ylabel(振幅);title(卷积所得输出); grid;x1 = x zeros(1,8);y1 = filter(h,1,x1);subplot(2,1,2);stem(n,y1);xlabel(时间序号n ); ylabel(振幅);title(滤

10、波生成输出); grid;没有差别，对x补零可以减少，增加抽样点，满足点数对应。Q2-32clf;num = 1 -0.8; den = 1 1.5 0.9;N = 200;h = impz(num,den,N+1);parsum = 0;for k = 1:N+1; parsum = parsum + abs(h(k); if abs(h(k) 10(-6), break, endendn = 0:N;stem(n,h)xlabel(时间序号n); ylabel(振幅);disp(值 =);disp(abs(h(k);对应的离散时间系统差分方程是：yn+1.5yn-1+0.9yn-2=xn-

11、0.8xn-1，该系统稳定取较大N值1000Q2-34clf;n = 0:299;x1 = cos(2*pi*10*n/256);x2 = cos(2*pi*100*n/256);x = x1+x2;num1 = 0.5 0.27 0.77;y1 = filter(num1,1,x); den2 = 1 -0.53 0.46;num2 = 0.45 0.5 0.45;y2 = filter(num2,den2,x); subplot(2,1,1);plot(n,y1);axis(0 300 -2 2);ylabel(振幅);title(系统输出#1); grid;subplot(2,1,2);plot(n,y2);axis(0 300 -2 2);xlabel(时间序号n); ylabel(振幅);title(系统输出#2); grid;第二个滤波器更好的抑制输入信号的高频分量。