信号与系统（英文版）_1 Signal and System

1 Signal and System 1. Signals and Systems 1.1 Continuous-time and discrete-time signals 1.1.1 EXamples and Mathematical Representation A. EXamples (1)Asimple RC circuit Source voltage Vs and C=N Capacitor voltage Vc

1 Signal and System 1.1 Continuous-time and discrete-time signals 1.1.1 Examples and Mathematical Representation A. Examples (1) A simple RC circuit Source voltage Vs and Capacitor voltage Vc 1. Signals and Systems

1 Signal and System (2)An automobile ⊙ pV Force f from engine Retarding frictional force pV Velocity V

1 Signal and System (2) An automobile Force f from engine Retarding frictional force ρV Velocity V

1 Signal and System 3)A Speech Signal MwhwiwhwwMwMMAi se

1 Signal and System (3) A Speech Signal

1 Signal and System (4)A Picture

1 Signal and System (4) A Picture

1 Signal and System 5)Vertical Wind profile 26 24 22 20 18 g16 14 B 10 02004006008001,0001,2001,4001,600 Height(feet)

1 Signal and System (5) Vertical Wind Profile

1 Signal and System B. Types of Signals (1)Continuous-time Signal

1 Signal and System B. Types of Signals (1) Continuous-time Signal

1 Signal and System (2)Discrete-time Signal 400 350 300 250 200 150 100 Jan.5,1929 Jan.4,1930

1 Signal and System (2) Discrete-time Signal

1 Signal and System C. Representation (1)Function Representation Example: x(t=cosopt ()=eo0 (2)Graphical Representation Example:( See page before

1 Signal and System C. Representation (1) Function Representation Example: x(t) = cos0 t x(t) = ej 0 t (2) Graphical Representation Example: ( See page before )

1 Signal and System 1.1.2 Signal Energy and Power A. Energy (Continuous-time Instantaneous power p(t)=v()()=v2(t)=Rt2(t) R Let r=1Q. so p()=i2(t)=v2(t)=x2(t)

1 Signal and System 1.1.2 Signal Energy and Power A. Energy (Continuous-time) Instantaneous power: ( ) ( ) 1 ( ) ( ) ( ) 2 2 v t R i t R p t = v t i t = =  Let R=1Ω, so p(t)=i2 (t)=v2 (t)=x2 (t)

1 Signal and System Energy over t1≤t≤t2: p()di (t )dt=x2(t)dt Total Energy Eoo=li x(t)dt Average Power: Po x(tdt 2T

1 Signal and System Energy over t1 t  t2 :    = = 2 1 2 1 2 1 ( ) ( ) ( ) 2 2 t t t t t t p t dt v t dt x t dt Total Energy:  →  = 2 1 ( ) 2 lim t t T E x t dt Average Power: − →  = T T T x t dt T P ( ) 2 1 2 lim