Categorization of Stochastic Processes 1 Discrete time; discrete variable 2 Discrete time; continuous variable 3 Continuous time; discrete variable 4 Continuous time; continuous variable Options, Futures, and Other Derivatives,4 4th edition2000 by John.hull Tang Yincai, 2003, Shanghai Normal University

4.1 periodic sampling 4.2 discrete-time processing of continuous-time signals 4.3 continuous-time processing of discrete-time signal 4.4 digital processing of analog signals 4.5 changing the sampling rate using discrete-time processing

2.1 Discrete-Time Signals: Time-Domain Representation Signals represented as sequences of numbers, called samples Sample value of a typical signal or sequence denoted as x[n] with n being an integer in the range-oo≤n≤∞ x[n] defined only for integer values of n and undefined for noninteger values of n Discrete-time signal represented by {x[n]}

◆2.0 Introduction ◆2.1 Discrete-Time Signals: Sequences ◆2.2 Discrete-Time Systems ◆2.3 Linear Time-Invariant (LTI) Systems ◆2.4 Properties of LTI Systems ◆2.5 Linear Constant-Coefficient Difference Equations

§4.1 LTI Discrete-Time Systems in the Transform Domain §4.2 The Frequency Response §4.3 Frequency Response Computation Using MATLAB §4.4 The Concept of Filtering §4.5 Phase and Group Delays §4.6 Frequency Response of the LTI Discrete-Time System §4.7 The Transfer Function §4.8 The Transfer Function §4.9 Frequency Response from Transfer Function §4.10 Types of Transfer Functions §4.11 Linear-Phase FIR Transfer Functions §4.12 Allpass Transfer Function §4.13 Minimum-Phase and Maximum-Phase Transfer Functions

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

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)

An LtI discrete-time- system is completely characterized in the time-domain by its impulse response {h[n]} We consider now the use of the DTFT and the z-transform in developing the transform- domain representations of an Lti system Copyright 2001, S. K. Mitra

深圳大学管理学院：《运筹学》课程教学资源（PPT课件讲稿）专题（计算机仿真）Discrete-Event仿真模型与分析 A Brief Introduction to Discrete-Event Simulation Modeling and Analysis

2.1 The Continuous-Time Fourier Transform 2.2 The Discrete-Time Fourier transform 2.3 the discrete-time periodic sequences in the frequency-domain 2.4 Relationship of DTFT and FT 2.5 Z-Transform