Analog Modulation Angle Modulation FM(Frequency Modulation) PM(Phase Modulation)
Analog Modulation Angle Modulation - FM(Frequency Modulation) - PM(Phase Modulation)
Angle modulation Nonlinear modulation Requires high bandwidth Good performance in the presence of noise Used in situations where BW is not a major concern and high SNR is required ■FM is used in High fidelity FM broadcasting s TV audio broadcasting Microwave carrier modulation Point-to-Point communications system
Angle modulation ◼ Nonlinear modulation ◼ Requires high bandwidth ◼ Good performance in the presence of noise ◼ Used in situations where BW is not a major concern and high SNR is required ◼ FM is used in ◼ High fidelity FM broadcasting ◼ TV audio broadcasting ◼ Microwave carrier modulation ◼ Point-to-Point communications system
Representation of PM and FM Complex envelope in angle modulated signal z(t)）=Ae Envelope is real:V(t)==(t)=4 Phase is linear function of message signal m(t) But,z(t)is nonlinear function of m(t) Angle-modulated signal ■u(t)=A.cos(2πft+0(t) Carrier is c(t)=cos(2zft) ■In text::z(t)=eo,c(t)=Acos(2πft)
Representation of PM and FM ◼ Complex envelope in angle modulated signal ◼ ◼ Envelope is real: ◼ Phase is linear function of message signal m(t) ◼ But, z(t) is nonlinear function of m(t) ◼ Angle – modulated signal ◼ ◼ Carrier is : ◼ In text: , ( ) ( ) j t c z t A e = ( ) ( ) V t z t A = = c ( ) cos(2 ( )) u t A f t t = + c c ( ) cos(2 ) c c t f t = ( ) ( ) j t z t e = ( ) cos(2 ) c c c t A f t =
Representation of PM and FM ■PM Phase is directly proportional to m(t) ■0(t)=k,m() ■k。:deviation constants of PM Or Phase sensitivity of PM FM Phase is proportional to the integral of m(t) )=2πk,m()d k,:deviation constants of PM
Representation of PM and FM ◼ PM ◼ Phase is directly proportional to m(t) ◼ ◼ : deviation constants of PM ◼ Or Phase sensitivity of PM ◼ FM ◼ Phase is proportional to the integral of m(t) ◼ ◼ : deviation constants of PM ( ) ( ) p t k m t = p k ( ) 2 ( ) t f t k m d − = f k
Relation between PM and FM Assume two message signal ·m,)for PM and m)for FM Then we have ■2πk∫'m,(r)dr=k,m,(0) aa k。dmn(t) 。m(0= 2πkdh We can generate PM from FM,and vice versa
Relation between PM and FM ◼ Assume two message signal ◼ mp (t) for PM and mf (t) for FM ◼ Then we have ◼ ◼ ◼ ◼ We can generate PM from FM, and vice versa 2 ( ) ( ) t f f p p k m d k m t − = 2 ( ) ( ) t f p f p k m t m d k − = ( ) ( ) 2 p p f f k dm t m t k dt =