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

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]}

§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

◆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

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

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

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)

◆7.0 Introduction ◆7.1 Design of Discrete-Time IIR Filters From Continuous-Time Filters ◆7.2 Design of FIR Filters by Windowing ◆7.3 Examples of FIR Filters Design by the Kaiser Window Method ◆7.4 Optimum Approximations of FIR Filters ◆7.5 Examples of FIR Equiripple Approximation ◆7.6 Comments on IIR and FIR Discrete-Time Filters

❖ 信号的描述 ❖ 信号的自变量变换 ❖ 基本信号 ❖ 系统及其数学模型 ❖ 系统的性质 1.0 引言 ( Introduction ) 1.1 连续时间与离散时间信号 （Continuous-Time and Discrete-Time Signals） 1.2 自变量变换 （Transformations of the Independent Variable) 1.3 复指数信号与正弦信号 （Exponential and Sinusoidal Signals ） 1.4 单位冲激与单位阶跃 （The Unit Impulse and Unit Step Functions） 1.5 连续时间与离散时间系统 （Continuous-Time and Discrete-Time Systems） 1.6 系统的基本性质 ( Basic System Properties )

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