1 Signal and System C. Time Scaling x(t) X(at)(a>0) Stretch if aso Compressed if a>0 x(2t (2) Example 1.1
1 Signal and System C. Time Scaling x(at) ( a>0 ) Stretch if a<0 Compressed if a>0 Example 1.1
1 Signal and System 1.2.2 Periodic Signals Definition There is a posotive value of T which x(t=x(t+T,for all t X(t is periodic with period T T— Fundamenta| Period For Discrete-time period signal xn]=x[n+N] for all n N— Fundamenta| Period
1 Signal and System 1.2.2 Periodic Signals Definition: There is a posotive value of T which : x(t)=x(t+T) , for all t x(t) is periodic with period T . T ⎯ Fundamental Period For Discrete-time period signal: x[n]=x[n+N] for all n N ⎯ Fundamental Period
1 Signal and System Examples of periodic signal (t) △AAA 0 2T X
1 Signal and System Examples of periodic signal
1 Signal and System 1.2.3 Even and odd signals Even signal: x (-t)=x(t or x[-n= x[n] Odd signal: x ()=-x(t or x[- n]=-xn] Even-Odd Decomposition Ev{x(t)}=x2(1)=[x(t)+x(-D) Ol{x(t)}=x(1)=[x(t)-x(t) or: Evin=xn==x[n+x[-ng Oa{x{n]}=x[n]={x[n]-x-H]}
1 Signal and System 1.2.3 Even and Odd Signals Even signal: x(-t) = x(t) or x[-n]= x[n] Odd signal : x(-t)= -x(t) or x[-n]= -x[n] Even-Odd Decomposition: [ ( ) ( )] 2 1 Ev{x(t)} x (t) x t x t = e = + − [ ( ) ( )] 2 1 Od{x(t)} x (t) x t x t = o = − − { [ ] [ ]} 2 1 Ev{x[n]} = xe [n] = x n + x −n { [ ] [ ]} 2 1 Od{x[n]} = xo [n] = x n − x −n or:
1 Signal and System Examples x-{on≤0 3-2 n<0 {x} 2 x(t) IT… <0 计11
1 Signal and System Examples