信号与系统（英文版）_8 Communication systems

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                   = − + + = − + + =

8 Communication systems Jω) oc Y(jω) (一ωc-ωM)-ωc(-ωc+ωk c-ωM)ω。(ωc+ωM

8 Communication systems

8 Communication systems Xjo Yu M

8 Communication systems

8 Communication systems 8.2 Demodulation for Sinusoidal am 8.2.1 Synchronous demodulation (1)Demodulation process H(jw w(t) 2 y(t) W cO Lowpass filter cos(uct +Oc)

8 Communication systems 8.2 Demodulation for Sinusoidal AM 8.2.1 Synchronous demodulation (1) Demodulation process

8 Communication systems In time domain w(t)=y(t)c(t) x(t)cos @,t x(t)+=x(t)cos 2@t In frequency domain W(j0)=X(j0)+X(j0-j20)+X(jo+2j2) Expected signal: x(t)or w(jo)

8 Communication systems ( 2 ) 4 1 ( 2 ) 4 1 ( ) 2 1 ( ) c c W j = X j + X j − j  + X j + j In frequency domain: x t x t t x t t w t y t c t c c   ( ) cos 2 2 1 ( ) 2 1 ( ) cos ( ) ( ) ( ) 2 = + = = In time domain: Expected signal: x(t) or W( j)

8 Communication systems (o C(jo) T 2 A)2

8 Communication systems