信号与系统课件第一章.ppt
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1、信号与系统 Signals and Systems,郝晓莉 陈后金 北京交通大学电子信息工程学院,Ch1 Introduction (绪论),本章重点: What is a signal? 什么是信号? What is a system? 什么是系统? Classifications of signals 信号的分类 Basic operations of signals 信号的基本运算 Basic signals 基本信号 Properties of systems 系统的特性,Ch1.1 What is a Signal (信号)?,A Speech signal Its amplitu
2、de varies with time, depending on the spoken word and who speaks it. Its a one-dimensional signal.,x(t),What is a Signal?,Electrocardiogram (ECG) Signal Represent the electrical activity of the heart. Its a one-dimensional signal.,x(t),What is a Signal?,I(x,y),An image is a function of two spatial c
3、oordinates. Its a two-dimensional signal.,What is a Signal (信号)?,Definitions,A Signal is formally defined as a function of one or more variables that conveys information on the nature of a physical phenomenon. 信号是一个或多个变量的函数,携带着某个物理现象的信息。,Ch1.2 What is a System(系统)?,A System is formally defined as an
4、 entity that manipulates one or more signals to accomplish a function, thereby yielding new signals.,Definitions,Ch1.3 Overview of Specific Systems,Elements of a communication system. The transmitter changes the message signal into a form suitable for transmission over the channel. The receiver proc
5、esses the channel output (i.e., the received signal) to produce an estimate of the message signal.,Examples: Communication Systems(通信系统),(a) Snapshot of Pathfinder exploring the surface of Mars.,(b) The 70-meter (230-foot) diameter antenna located at Canberra, Australia. The surface of the 70-meter
6、reflector must remain accurate within a fraction of the signals wavelength. (Courtesy of Jet Propulsion Laboratory.),Examples: Control Systems(控制系统),Block diagram of a feedback control system. The controller drives the plant, whose disturbed output drives the sensor(s). The resulting feedback signal
7、 is subtracted from the reference input to produce an error signal e(t), which, in turn, drives the controller. The feedback loop is thereby closed.,Examples: Biomedical Signal Processing (生物信号处理),The traces shown in (a), (b), and (c) are three examples of EEG signals recorded from the hippocampus o
8、f a rat. Neurobiological studies suggest that the hippocampus plays a key role in certain aspects of learning and memory.,(a) In this diagram, the basilar membrane in the cochlea is depicted as if it were uncoiled and stretched out flat; the “base” and “apex” refer to the cochlea, but the remarks “s
9、tiff region” and “flexible region” refer to the basilar membrane.,Examples: Auditory Systems(听觉系统),(b) This diagram illustrates the traveling waves along the basilar membrane, showing their envelopes induced by incoming sound at three different frequencies.,学习方法,理论与实际相结合,物理概念、数学概念和工程概念并重。 掌握信号与系统分析的
10、基本思想和方法;注意问题的提出、分析问题和解决问题的方法。 讲、练、做相结合;加强计算机实践环节,用 MATLAB进行信号与系统的分析。,本课程教学与学习的安排,1. 课堂教学:讲解重点内容和学生学习中遇到的疑难问题。 2. 作业: 书面作业(理论)+ MATLAB上机作业(实践)。 3. 期中和期末考试:闭卷形式。主要考察学生对本门课的基本理论基本原理及重点内容的掌握程度。 4.课程成绩的组成: 由书面作业、MATLAB作业、期中考试和期末考试4部分组成。,主要参考书,1 Simon H.,Barry V.V. Signals and Systems. John Wiley & Sons,I
11、nc.1999 2 Edward W.K.,Bonnie S.H. Fundamentals of Signals and Systems Using MATLAB. Prentice-Hall International,Inc. 1997 3 A.V.Oppenheim. Signals and Systems 或中译本(第2版). 西安交通大学出版社. 4 郑君里,应启珩等. 信号与系统. 第2版. 高等教育出版社,2000.,主要参考书,5 吴湘淇等. 信号、系统与信号处理(上). 第2版. 电子工业出版社,2001 6 吴湘淇,郝晓莉等. 信号、系统与信号处理软硬件 实现.电子工业出
12、版社,2002 7 陈后金等. 信号与系统. 清华大学出版社, 2003 8 陈后金等. 信号与系统学习指导与习题精解. 清华大学出版社,2004,Ch1.4 classifications of signals (信号的分类),1. continuous-time and discrete-time signals 连续时间信号和离散时间信号 2. periodic and non-periodic signals 周期信号和非周期信号 3. deterministic and random signals 确定信号和随机信号 4. Energy and power signals 能量信号
13、和功率信号,Continuous-time and Discrete-time signals 连续时间信号和离散时间信号,(a) Continuous-time signal x(t).,(b) Representation of x(t) as a discrete-time signal xn.,Continuous-time and Discrete-time signals 连续时间信号和离散时间信号,Discrete-time signal: a signal if it is defined only at discrete instants of time. 离散时间信号:若信
14、号仅在某些离散时刻处有定义, 用xn表示。,Continuous-time signal: a signal if it is defined for all time t. 连续时间信号:若信号在所有时间t 处都有定义, 用x(t)表示。,Definitions,Continuous-time and Discrete-time signals 连续时间信号和离散时间信号,离散信号可以由连续信号取样(sampling)得来: xn=x(t)|t=nT =x(nT) T称为取样间隔,periodic and non-periodic signals 周期信号和非周期信号,(a) Square
15、wave with amplitude A = 1 and period T = 0.2s. (b) Rectangular pulse of amplitude A and duration T1.,Periodic and Non-Periodic Signals (周期信号与非周期信号),A Periodic signals is a function of time that satisfies the condition: x(t+T) = x(t) for all t.,Definition,Fundamental Period: T0, the smallest value of
16、 T that satisfies the definition.,Period:,Periodic and Non-Periodic Signals (周期信号与非周期信号),Definition,Frequency,Fundamental Frequency,Angular Frequency,Periodic and Non-Periodic Signals (周期信号与非周期信号),(a) Square wave with amplitude A = 1 and period T = 0.2s. (b) Rectangular pulse of amplitude A and dura
17、tion T1.,Problem: Triangular wave alternative between 1 and +1,Periodic and Non-Periodic Signals (周期信号与非周期信号),A discrete Periodic signals is a function of time that satisfies the condition: xn+N = xn for integer n.,Definition,Fundamental Period: N, the smallest integer that satisfies the definition.
18、,Periodic and Non-Periodic Signals (周期信号与非周期信号),Definition,Period,Fundamental Frequency,(a) Discrete-time square wave alternative between 1 and +1. (b) Non-periodic discrete-time signal consisting of three nonzero samples.,periodic and non-periodic signals (周期信号和非周期信号),Deterministic and Random Signa
19、ls 确定性信号和随机信号(非确定性信号),Definitions,A random signal is a signal about which there is uncertainty before it occurs. 随机信号:再出现之前具有不确定性的信号。,A deterministic signal is a signal about which there is no uncertainty with respect to its value at any time. 确定性信号:在任意时刻都有确定的值的信号。,Deterministic and Random Signals 确
20、定性信号和随机信号,Deterministic and Random Signals 确定性信号和随机信号,t,t,t,X(t),Energy and Power signals (能量信号和功率信号),Definitions:,Energy,Average Power,Energy and Power signals (能量信号和功率信号),Definitions:,Energy Signal,Power Signal,Energy and Power signals 能量信号和功率信号,Problem: Determine the total energy of the discrete-
21、time signal.,Energy and Power signals (能量信号和功率信号),Problem: Determine the average power of the square wave.,amplitude A = 1 and period T = 4s, T0 = 1s.,Energy and Power signals (能量信号和功率信号),Energy signal? Power signal?,Ch1.5 basic operations on signals 信号的基本运算,1. 基于从变量(信号本身或信号之间)的运算 幅度变化; 相加和相乘; 连续信号的
22、微积分,离散信号的差分与累加 2. 基于自变量的运算 连续信号的翻转、展缩和平移 离散信号的翻转、展缩和平移,operations performed on dependent variables (基于从变量的运算),1. Amplitude scaling (幅度比例变化) x(t) cx(t) xn cxn (c为常数) 波形不变,幅度成比例放大或缩小。 Example:x(t)=sin(210t) ; y(t)=5x(t)=5sin(210t) ;,operations performed on dependent variables (基于从变量的运算),2. Addition (信
23、号相加) y(t) = x1(t)+x2(t) y(n) = x1n+x2n,3. Multiplication (信号相乘) y(t) = x1(t) x2(t) y(n) = x1n x2n,operations performed on dependent variables (基于从变量的运算),4. Differentiation(连续信号的微分) 5. integration(连续信号的积分),operations performed on dependent variables (基于从变量的运算),Example:电感两端的电压与其电流为微分关系: Example: 电容两端的
24、电压与其电流为积分关系:,operations performed on independent variables (基于信号自变量的运算),(a) continuous-time signal x(t) (b) version of x(t) compressed by a factor of 2, (c) version of x(t) expanded by a factor of 2.,1.Time scaling(尺度展缩): y(t)=x(at) a0 若01, 则x(at)是x(t)压缩a倍。,Time scaling(尺度展缩),(a) discrete-time signa
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