x() xs(t) 血■ ■由 0 Je -pxIs 1t) LPF x(t) e-nals f() -21 0 Figure 1.2 Baseband equivalent channel (at carrier frequencyf) h=0+i h,()=h,)e2e ■An alternative e x() ar referred to as the in-phase and quadrature components ofx().respectively,and are denoted by x,(t)=(t)and xo(1)=3x(t)).From (1.2),we have the in-phase and quadrature representation of a real signal given by x()=[(e =V29r[x,(0]cos(2πfI)-V2[x,)]小sin(2πf) =2x,(t)cos(2zft)-x(t)sin(2zft) 1.3) A quadrature modulator performing upconversion and a quadrature demodulator performing downconversion are shown in Fig1.3.respectivelv. ss(t】 1 [s(t) 反cos2mft[号 V2cos2af [s(】 S8( 1212 ⊗ 2 c j f t e π 2R[ ] channel xb(t) x(t) y(t) 2 () h t + ⊗ 2 c j f t e− π 0 fc xA(t) -fc 0 fc 0 fc xb(t) ⊗ 2 c j f t e− π y(t) xb(t) -2fc 0 LPF 2 () f t alternative 0 0 Figure 1.2 „ Baseband equivalent channel (at carrier frequency fc) 1 ˆ ( ) [ ( ) ( )] 2 A h t h t jh t = + 2 () () c j ft b A h t h te− π = „ An alternative representation of a real signal is derivative of the complex envelope representation. The real and imaginary parts of the complex envelope ( ) b x t are referred to as the in-phase and quadrature components of x(t), respectively, and are denoted by ( ) { ( )} I b x t xt = R and ( ) { ( )} Q b x t xt = I . From (1.2), we have the in-phase and quadrature representation of a real signal x(t) given by 2 () 2 () c j ft b xt x te π = ⎡ ⎤ R ⎣ ⎦ = − 2 ( ) cos(2 ) 2 ( ) sin(2 ) R I [ xb cb c t ft x t ft ] π π [ ] 2 ( )cos(2 ) 2 ( )sin(2 ) I cQ c = − x t ft x t ft π π (1.3) A quadrature modulator performing upconversion and a quadrature demodulator performing downconversion are shown in Fig. 1.3, respectively