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Ch1. Signals and Systems 1 1. Signals ? Signals: physical phenomena or physical quantities, which change with time or space. ? Functions of one or more independent variables. example: x(t ) 1) Definition and Mathematical Representation of Signals (信号的定义及其数学表示) A simple RC circuit: Ch1. Signals and Systems 2 A speech signal “ Should we chase ”这句话的声压随时间变化的波形 Ch1. Signals and Systems 3 A picture 一幅黑白照片可用亮度随二维空间变化的函数来表示 Ch1. Signals and Systems 4 2 ) Classification of Signals (信号的分类) (1) Determinate and Random Signals ? A determinate signal —— x(t ) ?能够用确定的时间函数表示。? A random signal —— cannot find a function to represent it ?不能用确定时间函数表示——干扰信号、噪声信号 Ch1. Signals and Systems 5 (2) Continuous-time and Discrete-time Signals ? continuous-time signals ’ independent variable is continuous : x(t )?对一切时间 t (除有限个不连续点外) 都有确定的函数值,这类信号就称为连续时间信号,简称连续信号。? discrete-time signals are defined only at discrete times ( only for integer values of the independent variable) : x[n ]?仅在不连续的瞬间(仅在自变量的整数值上)有确定函数值 Ch1. Signals and Systems 6 Representing Signals Graphically 0 x (t)t Graphical representations of (a) continuous-time and (b) discrete-time signals (a) -2x [-1] x [0] x [4] -4 -3 -1 0 1 2 3 4 5 x [n] n (b) Ch1. Signals and Systems 7 (3) Periodic and Aperiodic Signals 在较长时间内( 严格地说,无始无终) 每隔一定时间 T(或整数 N)按相同规律重复变化的信号叫周期信号。 For a continuous-time signal x(t ) x(t )= x(t+mT ) , (m=0,+1,-1,+2,-2, ……) for all values of t. For a discrete-time signal x[n ] x[n ]= x[n+mN ] , (m=0,+1,-1,+2,-2, ……) for all values of n . In this case , we say that x(t)(x[n ] ) is periodic with Fundamental Period T(N). Ch1. Signals and Systems 8 Examples of periodic signals: sin , cos etc. with their fundamental period N 0 =3 Ch1. Signals and Systems 9 Example Determine the fundamental period of the signal x(t ) = 2 cos (10 πt+ 1) -sin (4π t- 1). From trigonometry, we know that the fundamental period of cos (10 πt+ 1) is T 1 =