第二章离散时间信号和系统的频域分析 主要内容: 一、DT信号的离 Fourier散时间变换 二、周期序列的离散傅立叶级数及傅立叶变换表示式 三、序列的Z变换 四、利用Z变换分析信号和系统的频域特性

3.1 Discrete-Time Fourier Transform Definition- The discrete-time Fourier transform (DTFT) X(eio) of a sequence x[n] is given by jae In general,() is a complex function of the real variable and can be written as X(eio) Xre(eio) +j Xim(eio)

5.1 Digital Processing of Continuous-Time Signals Digital processing of a continuous-time signal involves the following basic steps: (1) Conversion of the continuous-time signal into discrete-time signal, ()Processing of the discrete-time signal, (3) Conversion of the processed discrete- time signal back into a continuous-time signal

6.1 Introduction The convolution sum description of an LTI discrete-time system can, in principle, be used to implement the system For an IR finite-dimensional system this approach is not practical as here the impulse response is of infinite length · However, direct implementation of the IIR finite-dimensional system is practica

Objective-Determination- of realizable transfer function G() approximating a given frequency response specification is an important step in the development of a digital filter If an IIR filter is desired, G() should be a stable real rational function Digital filter design is the process of deriving the transfer function G

Introduction Ideally, the system parameters along with the signal variables have infinite precision taking any value between -oo and · In practice, they can take only discrete values within a specified range since the registers of the digital machine where they are stored are of finite length

1.1 Introduction Any problems about signal analyses and processing may be thought of letting signals trough systems. f(t) y(t) h(t) From f(t) and h(t), find y(t), Signal processing From f(t) and y(t), find h(t), System design From(t)andh(t), find(t), Signal reconstruction

4.1 LTI Discrete-Time Systems in the Transform Domain · Such transformdomain- representations provide additional insight into the behavior of such systems It is easier to design and implement these systems in the transform-domain for certain applications We consider now the use of the DtFt and the z-transform in developing the transform- domain representations of an LTI system

1. Any arbitrary input sequence x[n] can be expressed as a linear combination of delaved and advanced unit sample sequences [n]=x[k][n-k] k=-0 2. .Linear Time-Invariant()System A system satisfying both the linearity and the time-invariance property. .If yiln] is the output due to an input xiln] and y2ln] is the output due to an input x2n] then for an input xn]=axiln]+bx2n] the output is given by ]=]+by2[n]

实验2离散系统的差分方程、冲激响应和卷积分析 实验目的:加深对离散系统的差分方程冲激响应和卷积分析方法 的理解。 实验原理:离散系统