信号英文版.ppt

CHAPTER 1 Signals and Systems
Signals: physical phenomena or physical quantities, which change with time or space.
Functions of one or more independent variables.
example: x(t)
Definition and Mathematical Representation of Signals
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Example of one-dimensional signal----the waveform of the song of a bird
Example of a two-dimensional signal----the picture of the Efil tower
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CLASSIFICATIONS OF SIGNALS
  Continuous-time and Discrete-time Signals
(连续时间和离散时间信号)
continuous-time signals’ independent variable is continuous : x(t)=e t
discrete-time signals are defined only at discrete times : x[n] =2n
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Representing Signals Graphically
Figure Graphical representations of
(a) continuous-time and (b) discrete-time signals
0
x(t)
t
(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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Periodic and Aperiodic Signals
(周期和非周期信号)
For a continuous-time signal x(t)
x(t) = x(t + T)
for all values of t.
For a discrete-time signal x[n]
x[n] = x[n + N]
for all values of n.
In this case, we say that x(t) (x[n]) is periodic with period T(N).
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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)?
If there is a rational T, and it is the mon multiple(最小公倍数) 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 is rational, so that the fundamental period of x(t) is 1.
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Determinate and Random Signals
(确定性信号和随机信号)
A determinate signal ——x(t)
A random signa