6 Time and Frequency Characterization of Signals and Systems

6.0 Introduction

Meanings of the Fourier Transform of a CT signal

Magnitude-Spectrum and Phase-Spectrum

( The magnitude and phase angle of the CTFT )

Meanings of the Frequency response of a LTI system

The magnitude and phase shift of the frequency response

(The magnitude-frequency and phase-frequency characteristics)

The distortionless transmission-system

The Time and Frequency-domain properties of Frequency-Selective Filters

Time and Frequency-domain properties of First and Second-Order systems

6.1 The Magnitude-Phase Representation of The Fourier Transform

( ) ( ) j tX j x t e dt

Magnitude-Spectrum/ The magnitude of the CTFT :

The complex magnitude of the frequency component is:

The relative complex magnitude is

1( ) ( )

2j tx t X j e d

( )X j

j te

1( )

2X j d

( )( ) ( ) j X jX j X j e

Phase-Spectrum/ The phase angle of the CTFT :

The complex magnitude of the frequency component is:

The relative complex magnitude is

1( ) ( )

2j tx t X j e d

( )X j

j te

1( )

2X j d

( )( ) ( ) j X jX j X j e

clear all; t=-4:0.05:4;

xt=cos(0.56*pi*t)+cos(0.28*pi*t)+cos(t);

plot(t,xt,'b'); xlabel('t'); hold on

y1t=cos(0.56*pi*t-pi/3)+cos(0.28*pi*t-2*pi/3)+cos(t-pi/2);

plot(t,y1t,'r');y2t=cos(0.56*pi*(t-0.5*pi/2))+cos(0.28*pi*(t-0.5*pi/2))+cos(t-0.5*pi/2);

plot(t,y2t,'c');title('x(t),y1(t),y2(t)');hold off

clear all; t=-4:0.05:4;

xt=cos(0.56*pi*t)+cos(0.28*pi*t)+cos(t);

plot(t,xt,'b'); xlabel('t'); hold on

y1t=0.25*cos(0.56*pi*t)+0.5*cos(0.28*pi*t)+cos(t); plot(t,y1t,'r')

y2t=cos(0.56*pi*t)+0.5*cos(0.28*pi*t)+0.25*cos(t);

plot(t,y2t,'c');title('x(t),y1(t),y2(t)'); hold off

6.2 The Magnitude-Phase Representation of The Frequency Response of LTI Systems

( )( ) ( ) ( ) j H jH j CTFT h t H j e

/1( ) ( )th t e u t

1/( )

1/H j

j

•The magnitude of the frequency response / The magnitude-frequency characteristic:

The effect an LTI system has on the magnitude of the FT of a input signal is to scale it by the magnitude of the frequency response

( )H j

( ) ( ) ( )Y j X j H j ( ) ( ) ( )Y j X j H j

•The phase shift of the frequency response / The phase -frequency characteristic: ( )H j

( ) ( ) ( )Y j X j H j ( ) ( ) ( )Y j X j H j

6.2.1 The distortionless transmission-system

the distortionless transmission-system

the distortionless

transmission-system

distortion

( )x t 0( ) ( )y t k x t t

6.2.1 The distortionless transmission-system

the distortionless transmission-system

( )x t 0( ) ( )y t k x t t 0

0

0

( )( )( )

( ) ( )

( ) ,

( ) ,

jtjtk X j eY j

H j k eX j X j

H j k

H j t

1 1 2 2( ) cos( ) 2 cos( )x t t t

1 1 1 0 2 2 2 0 0( ) cos( ) 2 cos( ) ( )y t k t t k t t k x t t

clear all; t=-4:0.05:4;

xt=cos(0.56*pi*t)+cos(0.28*pi*t)+cos(t);

plot(t,xt,'b'); xlabel('t'); hold on

y1t=cos(0.56*pi*t-pi/3)+cos(0.28*pi*t-2*pi/3)+cos(t-pi/2);

plot(t,y1t,'r');y2t=cos(0.56*pi*(t-0.5*pi/2))+cos(0.28*pi*(t-0.5*pi/2))+cos(t-0.5*pi/2);

plot(t,y2t,'c');title('x(t),y1(t),y2(t)');hold off

clear all; t=-4:0.05:4;

xt=cos(0.56*pi*t)+cos(0.28*pi*t)+cos(t);

plot(t,xt,'b'); xlabel('t'); hold on

y1t=0.25*cos(0.56*pi*t)+0.5*cos(0.28*pi*t)+cos(t); plot(t,y1t,'r')

y2t=cos(0.56*pi*t)+0.5*cos(0.28*pi*t)+0.25*cos(t);

plot(t,y2t,'c');title('x(t),y1(t),y2(t)'); hold off

SAS实验三线性失真的计算机仿真与分析

内容1 无失真传输系统的概念，应满足的条件；2 幅度失真的涵义，仿真分析；3 相位失真的涵义，仿真分析；4 幅度、相位失真的仿真分析；5 总结

要求1 理论分析完整、严谨；2 仿真条件表述清晰，仿真结果具有说服力；3 以学术论文格式写作。

文档类型： Word 或 PPT 文档 文件名：学号 _ 姓名 _ 实验 3