Chapter 3 Fourier series 93.5 Properties of Continuous-Time Fourier Series 93.5.1 Linearity x() y() z(t)=Ax(t)+By ( <s>ck=Aa+Bbk 53.5.2 Time Shifting x() x(t-to)<s>a,e kao 16
16 Chapter 3 Fourier Series §3.5 Properties of Continuous-Time Fourier Series §3.5.1 Linearity x t a y t b ( )⎯→ ⎯→ k k ( ) FS FS ( ) ( ) ( ) k k k z t Ax t By t c Aa Bb = + ⎯→ = + FS §3.5.2 Time Shifting ( ) k x t a ⎯→FS ( ) 0 0 0 jk t k x t t a e− − ⎯→FS
Chapter 3 Fourier series 93.5.3 Conjugation and Conjugate Symmetry (共轭及共轭对称性) rlt →anx(t) x()=x()→ak=aora=ak (a)x(t)=ao +2> A, cos(kOot +Ok) (b)x(t)=,+2>(B, cos koot-CK sin kO.t) x()=x:()→a=a,<0; 17
17 x(t) x (t) = §3.5.3 Conjugation and Conjugate Symmetry （共轭及共轭对称性） ( ) ( ) − ⎯→ k ⎯→a k x t a x t FS FS Chapter 3 Fourier Series k k a = a − x(t) x (t) = ak a−k or = k k a a = − k k a a − = − ( ) ( ) 0 0 ( ) 1 a 2 cos k k k x t a A k t + = = + + ( ) ( ) 0 0 0 ( ) 1 b 2 cos sin k k k x t a B k t C k t + = = + −