E210 Lecture Notes Dianguang Ma Spring 2010
EI210 Lecture Notes Dianguang Ma Spring 2010
Chapter 1 (Part Il) Signals and Systems
Chapter 1 (Part II) Signals and Systems
The Discrete-Time Unit Step Function 。Definition 1,n≥0 m=0.n<0
The Discrete-Time Unit Step Function • Definition 0, 0 1, 0 [ ] n n u n
The Discrete-Time Unit Step Function u[n] 1.099 n -4-3-2-1 01234
The Discrete-Time Unit Step Function
The Continuous-Time Unit Step Function ·Definition 1,t>0 u)=0,t<0
The Continuous-Time Unit Step Function • Definition 1, 0 ( ) 0, 0 t u t t
Continuous-time version of the unit-step function of unit amplitude. (t) -t 0
Continuous-time version of the unit-step function of unit amplitude
The Rectangular Pulse mw防-6小 rect(t)=u(t+0.5)-u(t-0.5)
The Rectangular Pulse 1, 0.5 rect( ) 0, 0.5 rect( ) ( 0.5) ( 0.5) t t t t u t u t
(a)Rectangular pulse x(t)of amplitude A and duration of 1 s,symmetric about the origin.(b)Representation of x(t)as the difference of two step functions of amplitude A,with one step function shifted to the left by and the other shifted to the right by %the two shifted signals are denoted by x1(f)and x2(f), respectively.Note that x(f)=x1(f)-x2(f). x()） x1(0 A -0.5 0 0.5 -1 -0.5 0 0.5 (a) (b) x2(I) A -1 -0.5 0 0.5 (c)
(a) Rectangular pulse x(t) of amplitude A and duration of 1 s, symmetric about the origin. (b) Representation of x(t) as the difference of two step functions of amplitude A, with one step function shifted to the left by ½ and the other shifted to the right by ½; the two shifted signals are denoted by x1 (t) and x2 (t), respectively. Note that x(t) = x1 (t) – x2 (t)
The Signum (or Sign)Function ag{ t>0 ,t<0 sgn(t)=-1+2u(t)
The Signum (or Sign) Function 1, 0 sgn( ) 1, 0 sgn( ) 1 2 ( ) t t t t u t
The Sampling/Sinc Function The sampling function Sa(t) sin(t) The sinc function Sinc(t) sin(xt）-Sa(πt)） πt
The Sampling/Sinc Function The sampling function sin Sa( ) The sinc function sin Sinc( ) Sa( ) t t t t t t t