义——连续时间傅立叶变换.ppt

Signals and Systems,Chapter 4 The Continuous-Time Fourier Transform Liu Ke, School of Automation Engineering,Review,Chapter 2:,Time-Domain:Convolution,Chapter 3:,Frequency-Domain:frequency response,Review,Chapter 4,Chapter 5,Chapter 9,Chapter 10,aperiodic continuous-time signal,aperiodic discrete-time signal,The contents of the chapter,The Fourier transform of aperiodic signal The Fourier transform of periodic signal The properties of Fourier transform Linear constant coefficients differential equation,4.1 Representation of aperiodic signal:the continuous-time Fourier transform,The envelop of The representation of Fourier transform Convergence of Fourier transform Some examples,Envelop of Tak,Development,Introduction,periodic,Chapter 3,aperiodic,Chapter 4,The key:,Fourier transform,Summary,Fourier series periodic signal Fourier transform aperiodic signal,4.1.2 Convergence of Fourier transform,View of energy finite energy(square integrable),The dirichlet conditions (1) x(t) absolutely integrable; (2) finite number of maxima and minima with any finite interval; (3) finite number of discontinuities with any finite interval;each of discontinuities must be finite,4.1.3 Example of continuous-time FT,Example 4.1,Example 4.2,Example 4.3,Example 4.4,Example 4.5,Duality property,4.2 The Fourier transform for periodic signals,Example 4.6,T=4T1,Example 4.7,Example 4.8,4.3 Properties of the continuous-time Fourier transform,4.3.1 Linearity 4.3.2 Time Shifting 4.3.3 Conjugation and Conjugate Symmetry 4.3.4 Differentiation and Integration 4.3.5 Time and Frequency Scaling 4.3.6 Duality 4.3.7 Parsevals Relation,4.3.1 Linearity,time shift dont change the magnitude of Fourier transform time shift is to introduce into a phase shift,Example 4.9,Determine the FT of x(t),Method 1:,Method 2:,4.3.3 Conjugation and conjugate symmetry,If x(t) is real,If x(t) is real and odd,If x(t) is real and even,If x(t) is real,Example 4.10,4.3.4 Differential and integral,Example 4.11,Example 4.12,4.3.4 Time and frequency scaling,Example 4.13,Some useful properties,4.3.7 Parsevals relation,Example 4.14,Assignments,4.3（b），4.4，4.6，4.8,4.4 The convolution property,The response of cascade system,h(t)、H(jw) completely characterize an LTI system,Example 4.15,The representation of LTI system,Example 4.20,Example 4.19,Partial fraction expansion,The roots of denominator polynomial are different,The roots of denominator polynomial are same,4.5 The multiplication property,Example 4.21,Example 4.22,Example 4.23,4.5.1 Frequency-selective filtering with variable center frequency,Assignments,4.10，4.11，4.14，4.15，4.18，4.19，4.24，4.25，4.28（a），4.32（a）（b）,4.7 System characterized by linear constant-coefficient differential equations,Example 4.26,SUMMARY,Fourier transform (aperiod/period) The properties of FT Linear constant-coefficient differential equations,Example,Example,x(t),t,-1,0,1,2,3,1,-1,Example,h1(t)