信号与系统第六章课件.ppt

1、1Time and Frequency Characterizationof Signals and SystemsChapter 62 th txjHjX tyjY Chapter 6 Time and Frequency Characterization thtxtyTime-Domain: jHjXjYFrequency-Domain:6.1 The Magnitude-Phase Representation （ 幅度幅度-相位）相位） of the Fourier TransformjXjejXjX dejXtxtj 21jXMagnitude 2jXEnergy-Density3

2、tttx6cos2cos41 tttx6cos42cos2 Chapter 6 Time and Frequency Characterization4 Chapter 6 Time and Frequency Characterization -1 0 1 1jX1 tttxsin1 -11 -10 9 0 9 10 11 1jX2 ttttx10cossin225( )cos()cos()cos()12312124623x tttt 032112, 8, 432193. 0, 7 . 2, 63212 . 7, 1 . 4, 2 . 1321 Chapter 6 Time and Freq

3、uency Characterization6 Chapter 6 Time and Frequency Characterization2. A black-and-white picture F1212,x t tXjj 2 21 1121212,jtjtXjjx t teedt dt Figure 6.2712(,)X jj 12|(,)|X jj Chapter 6 Time and Frequency Characterization8:|(,)|:(,)12120MagnitudeX jjPhaseX jj :|(,)|:(,)12121MagnitudeX jjPhaseX jj

4、 Chapter 6 Time and Frequency Characterization9Magnitude Chapter 6 Time and Frequency Characterization:(,)12 PhaseX jj 10 Chapter 6 Time and Frequency Characterization6.2 The Magnitude-Phase Representation of the Frequency Response of LTI Systems YjXjHj YjXjHj YjXjHj Hj Gain Hj Phase Shift6.2.1 Line

5、ar and Nonlinear Phase1. Linear Phase0 tjejH1jH0 tjH0 tjXjY11 Chapter 6 Time and Frequency Characterization ttttx3coscos3/cos3/3/3/3/21213/cosjjtjjteeeet 1cos2121costeeeetjjtjjt13cos21213cos3333teeeetjtjjtj 13cos1cos3/1costttty jejHjH1jH2. Nonlinear Phase 11jjjH1jHtg-jH-123/1cost12 Chapter 6 Time an

6、d Frequency Characterization3/323/3/323/21213/cosarctgjjtarctgjjteeeet 3/23cos2/cos3/3/costttty tx tyt03/3/cost 33/23cos2/cos3/3/costttty3/3/13 Chapter 6 Time and Frequency Characterization6.2.2 Group delay （群延时）（群延时）Consider a narrowband signal 窄带信号窄带信号02 0 2 0 00jXjHjjeejHjXjYGroup delay at =0 The

7、 Group Delay at each frequency jHdd0140()()tsignal delay Example:0( )()y tx tt 0()Hjt 0()jtHje Chapter 6 Time and Frequency Characterization15 Chapter 6 Time and Frequency CharacterizationExample 6.1 Consider an all-pass system.jHjHi31iiiiiiijjjjjH/2/1/2/122i11ijHjHiiff /21/1/22iiiitgjHjHjHi31i058.

8、0033. 0066. 0 30015050321321HzfHzfHzfLet Figure 6.516 Chapter 6 Time and Frequency Characterization6.2.3 Log-Magnitude and Bode Plots对数模和波特图对数模和波特图jHjXjYlogloglogBode Plots：Log-FrequencyLog-MagnitudesinjHjHjHlog17 Chapter 6 Time and Frequency CharacterizationExample txtydttdy/1/1jjH22/1/1jH22/1/1lg2

9、0lg20jH 0lg20 /1 ajH lg20lg20lg20 /1 bjHIt is approximately a linear function of lg()18dB/dec 20dB 30lg20lg20dB 3lg20/ 1jH Chapter 6 Time and Frequency CharacterizationdB 0dB 20dB 40dB 6001100010010jHlg20lg119 Chapter 6 Time and Frequency Characterization6.3 Time-Domain Properties of ideal Frequency

10、-Selective Filters01cjHc0jH01cjHc0ccjH ttthcsinct thAll-pass system with linear phase20 Chapter 6 Time and Frequency Characterization6.4 Time-Domain and Frequency-Domain Aspects of Nonideal filtersjX1jX2overlap1. Gradual transition from passband to stopband.2. The step response approaches a constant

11、 value without oscillations.3. When filtering is to be carried out in real time, causalityis a necessary constraint.4. In many contexts, we just need a simple filter.21 Chapter 6 Time and Frequency CharacterizationNonideal FilterPassband ripple 12Stopband ripple 2 tsThe unitresponsejHMagnitude2overshootRise time rtsttSetting time1111TransitionPassbandStopband2022 Chapter 6 Time and Frequency CharacterizationHomework: 6.5 6.23 6.27