信号与系统课件第五章

单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,CHAPTER 5,THE DISCRETE-TIME FOURIER TRANSFORM,5.0 INTRODUCTION,Discrete-time Fourier transform and inverse Fourier transform.,Similarities and differences between continuous-time and discrete-time Fourier transforms.,5.1 REPRESENTATION OF APERIODIC SIGNALS:THE DISCRETE-TIME FOURIER TRANSFORM,As,N,N,1,0,N,2,N,n,N,1,0,N,2,x,n,n,Defining a function:,Thus,Consequently,As,discrete-time Fourier transform,discrete-time inverse Fourier transform,Differences between the continuous-time and discrete-time Fourier transform are:,periodicity,of the discrete-time transform and the,finite interval,of integration in the synthesis equation.,In discrete time,Low frequencies,are the values of,near,even multiple of,;,high frequencies,are those values of,near,odd multiples of,.,2,0,2,2,0,2,0,n,x,1,n,0,n,x,2,n,Example 5.1,Consider the signal,1/(1),1/(1+),2,0,2,2,0,2,1,0,0,-1,1/(1+),1/(1),2,0,2,2,0,2,Example 5.2,Consider the signal,0,x,n,n,(1+)/(1),(1)/(1+),2,0 2,for,0,2,M,1/,N,s,2,spectrum of sampled signal with,s,2,M,In discrete-time case,the result of sampling theorem also exist.,Example 5.14,Consider a sequence,x,n,whose Fourier transform,Determine the,lowest rate,at which,x,n,may be sampled without aliasing.,Since,the corresponding sampling frequency is 2,/4=,/2.,So that,Thus,From the sampling theorem,we know,5.10 SUMMARY,The Fourier transform for periodic discrete-time signals;,The Fourier transform for,aperiodic,discrete-time signals;,Convenient way to obtain the frequency response and sample response of a discrete-time LTI system;,Fourier analysis method(also referred to frequency-domain analysis)(which is to used to change a linear constant-coefficient difference equation to an algebraic form);,The difference between the continuous-time Fourier transform and the discrete-time Fourier transform(the discrete-time Fourier transform of an,aperiodic,signal is always periodic with period 2,);,The properties of the Fourier transform(how different characteristics of signals are reflected in their transforms);,Sampling of discrete-time signals.,