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1、Chapter 6 Time and Frequency Characterization of Signals and SystemsSchool of Electronics & Information Engineering, South China University of Technology 6.1 The Magnitude-phase Representation of the Fourier TransformFor signal x(t) : 6 Time and frequency characterization of S&S 6 Time and frequency
2、 characterization of S&S 6 Time and frequency characterization of S&S 6 Time and frequency characterization of S&S 6 Time and frequency characterization of S&S6.2 The Magnitude-phase Representation of the Frequency Response of LTI SystemSystem characterization:Impulse responseFrequency response 6 Ti
3、me and frequency characterization of S&S6.2.1 Linear and Nonlinear PhaseLinear phase:Nonlinear phase:Example:Effect: Linear phase means non-distortion of signal transmission. 6 Time and frequency characterization of S&SNote: In the discrete-time case, a linear phase shift with an integer slope corre
4、sponds to a shift of xn by an integer number of samples.( Linear phase )( Nonlinear phase )( Original signal ) 6 Time and frequency characterization of S&SNon-distortionDistortion6.2.2 Group DelayDefinition:Example:Distortionless system: is a constant. 6 Time and frequency characterization of S&SNot
5、e: The phase slope tells us the size of the time shift. To examine the effects of the phase of a CT-LTI system on a small band of frequencies centered at = 0 , we can approximate the phase of this system in the band with the linear approximation 6 Time and frequency characterization of S&SDistortion
6、less System Which means that the frequency responseAll pass system:time domain 0 frequency domain 0Conditions (distortionless): 6 Time and frequency characterization of S&SExample:Non-constant group delay(abscissa)(ordinate)6.2.3 Log-Magnitude and Bod PlotsMagnitude spectrum:Phase spectrum: 6 Time a
7、nd frequency characterization of S&S(Ordinate Abscissa)(Unit: dB decibel) 6 Time and frequency characterization of S&SA typical Bode plotContinuous-time Ideal Frequency-selective Filters LowpassHighpassBandpassBandstop6.3 Time-Domain Properties of Ideal Frequency-selective Filters 6 Time and frequen
8、cy characterization of S&S-2-0-Discrete-time Ideal Frequency-selective Filters 6 Time and frequency characterization of S&SLowpassHighpassBandpassBandstopLowpass filter:(1) Continous-time:(2) Discrete-time: 6 Time and frequency characterization of S&S 6 Time and frequency characterization of S&SZero
9、 phase 6 Time and frequency characterization of S&S 6 Time and frequency characterization of S&SContinuous-time ideal lowpass filter with linear phase characteristic 6 Time and frequency characterization of S&SStep response of continuous-time ideal lowpass filterLetAsNon-causal system 6 Time and fre
10、quency characterization of S&SStep response of discrete-time ideal lowpass filter6.4 Time-Domain and Frequency-domain Aspects of Non-ideal FiltersBasic parameter of lowpass filter: 6 Time and frequency characterization of S&S1 passband ripple 2 stopband ripple p passband edge s stopband edge 6 Time
11、and frequency characterization of S&S 6 Time and frequency characterization of S&SExample of a 5th-orderButterworth filter and a 5-order Elliptic filter 6 Time and frequency characterization of S&SUnit step response6.5 First-Order and Second-Order Continuous-Time Systems 6 Time and frequency charact
12、erization of S&SHigh-order LTI systems are frequently represented by combining first-order and second-order systems in cascade or parallel arrangements. Consequently, the properties of first- and second-order systems play an important role in analyzing, designing higher order systems. LCCDE for LTI
13、system 6 Time and frequency characterization of S&S6.5.1 First-Order Continuous-Time SystemsDifferential equation:Frequency response:Impulse response:As is decreased, the impulse response h(t) decays more sharply. 6 Time and frequency characterization of S&SStep response:As is decreased, the rise ti
14、me of the step response s(t) becomes shorter, i.e., it rises more sharply toward its final value.Bode plot of the frequency response:For i.e.,while for 6 Time and frequency characterization of S&Si.e., we have , the magnitude is approximatelya linear function of lg, that it The low-frequency asympto
15、te is just the 0-dB line, while the high-frequency asymptote corresponds to a decrease of 20dB in for every decade in .(每10倍频程-20dB) 6 Time and frequency characterization of S&Sis often referred to as the break frequencywherePhase spectrum： 6 Time and frequency characterization of S&S，For，For，ForProblems: 6.5 6.23 6.27 6 Time and frequency characterization of S&S
