电子科技大学电子工程学院：《信号与系统》课程教学资源（PPT课件讲稿，英文版）Chapter 5 THE DISCRETE-TIME FOURIER TRANSFORM

Chapter 5 The discrete-Time Fourier transform CHAPTER 5 THE DISCRETE-TIME FOURIER TRANSFORM

1 CHAPTER 5 THE DISCRETE-TIME FOURIER TRANSFORM Chapter 5 The Discrete-Time Fourier Transform

Chapter 5 The discrete-Time Fourier transform Consider a discrete-time lti system: Eigenfunction 特征函数 H H(x)=∑kn— Eigenvalue(特征值) xn]=xn+n@%=2r/N x∑a”=∑% k=<N> 2兀 j y=∑ S keko).iko,n ∑ ahle k

2 Chapter 5 The Discrete-Time Fourier Transform hn yn n z n z ( ) n H z z Eigenfunction 特征函数 ( )   ——Eigenvalue (特征值） n n H z h n z − + =− =  Consider a discrete-time LTI system: xn= xn+ N 0 = 2 / N   n N jk k k N jk n k k N x n a e a e   2  0  =  =  = =   ( ) N jk N jk k k N jk jk n k k N y n a H e e a H e e     2 2 0 0         =  =  =  = 

Chapter 5 The discrete-Time Fourier transform N N2 N 0 Discrete-time Fourier transform pair x{] tejo lejon do Synthesis equation 2丌J2丌 eo)=∑xlp Xle Analysis equation n=-

3 Chapter 5 The Discrete-Time Fourier Transform Discrete-time Fourier transform pair   ( )      x n X e e d j j n  = 2 2 1 ( )   j n n j X e x n e  −  + =− =  Synthesis equation Analysis equation

Chapter 5 The discrete-Time Fourier transform onvergence ssues Associated with the Discrete-Time Fourier Transform 1. xn is absolutely summable, ∑x[|<∞ 2. xin] has finite energy. <OO n=-0 Discrete-time r(eio)=x(eio H(eio) Fourier Analysis F-Y 4

4 Chapter 5 The Discrete-Time Fourier Transform Convergence Issues Associated with the Discrete-Time Fourier Transform   n x n + =−    1. is absolutely summable, xn 2. has finite energy, xn      + =− 2 x n n ( ) ( ) ( ) j j j Y e = X e H e    ( )  1 F - j y n Y e  = Discrete-time Fourier Analysis

Chapter 10 The z-transform CHAPTER 10 THE Z-TRANSFORM

5 Chapter 10 The Z-Transform CHAPTER 10 THE Z-TRANSFORM