浙工大信号与系统.ppt

Chapter 5 The Discrete-Time Fourier Transform 5.0 INTRODUCTION 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 … … –N –N1 0 N2 N n –N1 0 N2 x[n] n 5.1.1 Development of the Discrete-Time Fourier Transform Defining As discrete-time Fourier transform discrete-time inverse Fourier transform periodicity of finite interval of integration in the synthesis equation. Discrete-time Fourier transform pair synthesis equation analysis equation In discrete time Low frequencies are the values of ω near even multiple of π ; high frequencies are those values of ω near odd multiples of π. –2π–π 0 π 2π ω –2π –π 0 π 2π ω 0 n x1[n] 0 n x2[n] Example 5.1 –2π –π 0 π 2π ω –2π –π 0 π 2π ω 0a1 -1a0 –2π –π 0 π 2π ω –2π –π 0 π 2πω 1/(1–a) 1/(1+a) 1/(1–a) 1/(1+a) Example 5.2 0 x[n] n –2π 0 2π ω for 0 a 1 (1+a)/(1–a) (1-a)/(1+a) Example 5.3 rectangular pulse –N10 N1 x[n] 1 n 5 –2π –π 0 π 2π ω 5.2 The Fourier Transform For Periodic Signals 2π (ω0–4π) ω0 (ω0+4π) (ω0–2π) (ω0+2π) ω … … arbitrary periodic sequence x[n] with period N Example 5.5 π –2π –ω0 0 ω0 2π (–2π–ω0) (–2π+ω0) (2π–ω0) (2π+ω0) ω … … Example 5.5 periodic sample train –N 0 N 2N n x[n] 1 … … 2π/N ω … … 5.3 Properties of The Discrete-Time Fourier Transform 5.3.1 Periodicity of the Discrete-Time Fourier Transform 5.3.2 Linearity of the Fourier Transform If then 5