8 Communication systems 8. Communication Systems 8. 1 Complex Exponential and Sinusoidal Amplitude modulation Modulating system model c(t) y(t=x(tc(t) X(t-modulating signal :t-carrier signal
8 Communication systems 8.1 Complex Exponential and Sinusoidal Amplitude Modulation Modulating system model: 8. Communication Systems x(t) c(t) y(t)=x(t)c(t) x(t) --- modulating signal c(t) --- Carrier signal
8 Communication systems 8. 1.1 Amplitude Modulation with Complex Exponential Carrier (1)Modulation Theory Exponential carrier: c(t=e For convenience, let 0c=0, so c(t)=e Output signal( modulated signal): y(t=x(te! Y(o=X(o)*C(o) 2元 C()=26(-Ol) Y(o=X(o-jo)
8 Communication systems 8.1.1 Amplitude Modulation with Complex Exponential Carrier Exponential carrier: For convenience, let c =0, so ( ) ( ) c c j t c t e + = j t c c t e ( ) = Output signal(modulated signal): j t c y t x t e ( ) = ( ) ( ) ( ) ( ) 2 ( ) ( )* ( ) 2 1 ( ) c c Y j X j j C j Y j X j C j = − = − = (1) Modulation Theory
8 Communication systems X(jo) CUw) ZTT
8 Communication systems
8 Communication systems (1)Implementation y(t=x(te' x(t)cos@t+jx(t)sin @t cos(ωt+6c RRe y(t)I 9m{y(t)} sin(oct+8c)
8 Communication systems x t t j x t t y t x t e c c j t c ( ) cos ( )sin ( ) ( ) = + = (1) Implementation
8 Communication systems 8.1.2 Amplitude Modulation with Sinusoidal signal cos(oct+Ac For convenience. choose 0=0.so y(t=x(t)c(t)=x(t)cos@ t Y(o) X(*(o) C(O)=xo(-)+x6(+l) Y()=2X(m-Jo.)+2X(O+1o)
8 Communication systems 8.1.2 Amplitude Modulation with Sinusoidal signal For convenience, choose c =0, so y t x t c t x t t c ( ) = ( ) ( ) = ( )cos ( ) 2 1 ( ) 2 1 ( ) ( ) ( ) ( ) ( )* ( ) 2 1 ( ) c c c c Y j X j j X j j C j Y j X j C j = − + + = − + + =