文档介绍：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:
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A speech signal
“Should we chase”这句话的声压随时间变化的波形
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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
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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
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(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
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Representing Signals Graphically
0
x(t)
t
Graphical representations of (a) continuous-time and (b) discrete-time signals
(a)
-2
x[-1]
x[0]
x[4]
-4
-3
-1
0 1 2 3 4 5
x[n]
n
(b)
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(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).
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Examples of periodic signals: sin, cos etc. with their fundamental period
N0=3
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Example Determine the fundamental period of the signal x(t) = 2cos(10πt+1)-sin(4πt-1).
From trigonometry, we know that the fundamental period of cos(10πt+1) is T1=1/5, and sin(4πt-1) is T2=1/2. What about the fundamental period of x(t)?
The answer is if there is a rational T, and it is the mon multiple of T1 and T2, then we say that x(t) is periodic with fundamental period T, or else, x(t) is aperiodic.
For the x(t) in this example, the mon multiple of and is unit 1, and it i