发布时间 : 星期四 文章信号与系统实验报告实验三 连续时间LTI系统的频域分析更新完毕开始阅读838c03dc00d276a20029bd64783e0912a3167c4d
信号与系统实验报告实验三 连续时间LTI系统的频域分析
图Q3-2
您编写的程序Q3_2抄写如下:% Q3_2
b = input('Type in the right coefficient vector of differential equation:'); % The coefficient vector of the right side of the differential equation
a = input('Type in the left coefficient vector of differential equation:'); % The coefficient vector of the left side of the differential equation w=-10:0、01:10;
H= freqs(b,a,w); % Compute the frequency response H Hm = abs(H); % Compute the magnitude response Hm phai = angle(H); % Compute the phase response phai
Hr = real(H); % Compute the real part of the frequency response
Hi = imag(H); % Compute the imaginary part of the frequency response subplot(221);
plot(w,Hm); grid on, title('Magnitude response'), xlabel('Frequency in rad/sec'); subplot(223);
plot(w,phai); grid on, title('Phase response'), xlabel('Frequency in rad/sec'); subplot(222);
plot(w,Hr); grid on, title('Real part of frequency response'); xlabel('Frequency in rad/sec'); subplot(224);
plot(w,Hi); grid on, title('Imaginary part of frequency response'); xlabel('Frequency in rad/sec');
执行程序Q3_2,输入信号x(t) = sin(t) + sin(8t),输入由Eq、3、3描述的系统。得到的图形如下:
信号与系统实验报告实验三 连续时间LTI系统的频域分析
此处粘帖执行程序Q3_2所得到的图形
Magnitude response151050-1021.510.5-505Frequency in rad/secPhase response10-50510Frequency in rad/secImaginary part of frequency response1050-5-505Frequency in rad/sec10-10-10-505Frequency in rad/sec100-10Real part of frequency response210-1-2-10
请手工绘制出信号x(t) = sin(t) + sin(8t) 的幅度频谱图如下:
您手工绘制的信号x(t) = sin(t) + sin(8t) 的幅度频谱图与执行程序Q3_2得到的x(t) = sin(t) +
sin(8t) 的幅度频谱图就是否相同？如不同,就是何原因造成的？
答:
执行程序Q3_2得到的x(t) = sin(t) + sin(8t) 的幅度频谱图实际上就是另外一个信号x1(t)的幅度
频谱,这个信号的时域数学表达式为 x1(t) =
请利用傅里叶变换的相关性质计算并绘制信号x1(t)的幅度频谱图。
计算过程:
手工绘制的x1(t) 的幅度频谱图如下:
结合所学的有关滤波的知识,根据上面所得到的信号的时域与频域图形,请从时域与频域两个方
面解释滤波的概念。
答:
信号与系统实验报告实验三 连续时间LTI系统的频域分析
Q3-3 编写程序
Q3_3,能够接受从键盘输入的系统微分方程系数向量,并分别绘制所给三个系
统的群延时曲线图。
抄写程序Q3_3如下:% Q3_3
b1 = input('Type in the right coefficient vector of differential equation:'); % The coefficient vector of the right side of the differential equation
a1= input('Type in the left coefficient vector of differential equation:'); % The coefficient vector of the left side of the differential equation
b2 = input('Type in the right coefficient vector of differential equation:'); % The coefficient vector of the right side of the differential equation
a2= input('Type in the left coefficient vector of differential equation:'); % The coefficient vector of the left side of the differential equation
b3 = input('Type in the right coefficient vector of differential equation:'); % The coefficient vector of the right side of the differential equation
a3= input('Type in the left coefficient vector of differential equation:'); % The coefficient vector of the left side of the differential equation w=-10:0、01:10;
H1 = freqs(b1,a1,w); % Compute the frequency response H phi1 = angle(H1);
H2 = freqs(b2,a2,w); % Compute the frequency response H phi2 = angle(H2);
H3 = freqs(b3,a3,w); % Compute the frequency response H phi3 = angle(H3);
tao1= grpdelay(b1,a1,w); tao2= grpdelay(b2,a2,w); tao3= grpdelay(b3,a3,w); subplot(321);
plot(w,phi1); grid on, title('Phase response of num1'); subplot(323);
plot(w,phi2); grid on, title('Phase response of num2'); subplot(325);
plot(w,phi3); grid on, title('Phase response of num3'), xlabel('Frequency in rad/sec'); subplot(322);
plot(w,tao1); grid on, title('Group delay of num1'); subplot(324);
plot(w,tao2); grid on, title('Group delay of num2'); subplot(326);
plot(w,tao3); grid on, title('Group delay of num3'); xlabel('Frequency in rad/sec');
系统Eq、3、1的群延时曲线图 系统Eq、3、3的群延时曲线图
信号与系统实验报告实验三 连续时间LTI系统的频域分析
Phase response of num150-5-1050-5-1050-5-10-1.8-2-2.2-1010-1-10-4-6-8-10Group delay of num1-50510-50510Phase response of num2Group delay of num2-50510-50510Phase response of num3Group delay of num3-505Frequency in rad/sec10-505Frequency in rad/sec10
根据上面的群延时曲线图可以瞧出,对系统
Eq、3、1,当频率为5弧度/秒时,群延时为 秒,
当频率为10弧度/秒时,群延时为 秒,如何解释这两个群延时时间？
根据上面的群延时曲线图,说明这两个系统就是否会造成对信号的相位失真？为什么？ 从系统Eq、3、3的群延时曲线图中可以瞧出,当信号的频率为1弧度/秒时,系统Eq、3、3对这
一频率的信号的延时就是 秒。所以,执行程序Q3_2时,当作用于系统Eq、3、3的输入信号为x(t) = sin(t) + sin(8t)时,其输出信号y(t)的数学表达式为:
四、实验报告要求
1、按要求完整书写您所编写的全部MATLAB程序
2、详细记录实验过程中的有关信号波形图(存于自带的U盘中),图形要有明确的标题。全部的MATLAB图形应该用打印机打印,然后贴在本实验报告中的相应位置,禁止复印件。
3、实事求就是地回答相关问题,严禁抄袭。
本实验完成时间: 年 月 日