5.aSymmetric sideband signals The normalized average power of the ussB signal is g m()+m)/ A2(m2(1)+m2(t (m()=m() The ssB signal power is the power of the modulating e signal (m2(t)) multiplied by the power gain factorA The normalized peak envelope power(PEp)is: (12)max(g(o)}=(/2)fmax{m2(O)+[mi(2 21
21 5.5Asymmetric sideband signals • The normalized average power of the USSB signal is ( ) ( ) ˆ ( ) 2 1 | ( ) ˆ( )| 2 1 ( ) 2 1 ( ) 2 2 ˆ ( ) ( ) 2 2 2 2 2 2 2 2 2 A m t A m t m t s t g t A m t m t c m t m t c c = = = + = = + • The SSB signal power is the power of the modulating signal〈m2 (t)〉multiplied by the power gain factor Ac . • The normalized peak envelope power (PEP) is : (1/ 2)max{ ( ) } (1/ 2) max{ ( ) [ ˆ( )] } 2 2 2 2 g t A m t m t = c +
5.aSymmetric sideband signals Baseband vI(t=Accos(oct) processing m(t) Modnation phase p +平 SSB signal hift across band of m(t vI(t V2(t)= Acsin(oct) Oscillator 90° phase f=f shift at f=f a) phase method Sideband filter m(t) bandpass filter on Modulation either upper or SsB signal Inpu lower sideband) Oscillator b)filter method Fig 5-5 Generation of ssB 22
22 5.5Asymmetric sideband signals • Fig. 5-5 Generation of SSB m(t) Modulation input -900 phase shift across band of m(t) Baseband processing Oscillator f=fc -900 phase shift at f=f c + + s(t) SSB signal m(t) v1(t) v1(t) =Accos(ωct) v2(t)= Acsin(ωct) a) phase method Sideband filter (bandpass filter on either upper or lower sideband) Oscillator f=fc m(t) Modulation input s(t) SSB signal b)filter method
5.aSymmetric sideband signals SSB signals have both am and pm. the am component (real envelope)is: r(t=8o=Avm2(t)+(m(oI · The Pm component is (1)=∠8(t)=tan 土mn( m() SSB signals may be received by using a super- heterodyne receiver that incorporates a product detector with 00=0, thus the receiver output is out KReg(t)e o)=KAm(t) Where k depends on the gain of the receiver and the loss in the channel. In detecting SSb signals with audio modulation, the reference phase 0o does not have to be zero, because the same intelligence is heard regardless of the value of the phase used, For digital modulation, the phase has to be exactly correct so that the digital waveshape is 23 ● preserved
23 5.5Asymmetric sideband signals • SSB signals have both AM and PM. The AM component (real envelope) is: 2 2 R(t) g(t) A m (t) [m ˆ(t)] = = c + • The PM component is ] ( ) ˆ( ) ( ) ( ) tan [ 1 m t m t t g t = = − • SSB signals may be received by using a super- heterodyne receiver that incorporates a product detector with θ0=0, thus the receiver output is: Re{ ( ) } ( ) 0 v K g t e KA m t c j out = = − • Where K depends on the gain of the receiver and the loss in the channel. In detecting SSB signals with audio modulation, the reference phase θ0 does not have to be zero, because the same intelligence is heard regardless of the value of the phase used, For digital modulation, the phase has to be exactly correct so that the digital waveshape is preserved
5.5Asymmetric sideband signals (V estigial sideband DBS VBS Filter SysB(r) Filter) Modulation Modulator (a) Generation of vsB Signal SO) (b)Spectrum of DSB Signal (c)Transfer Function of vsB Filter f (d)Spectrum of vsB Signal HC-fc)+ H,C+fe)i fc) H,C+fc (e) vsB Filter Constraint Figure 5-6 VSB transmitter and spectra
24 5.5Asymmetric sideband signals (Vestigial sideband)
5.aSymmetric sideband signals (Vestigial sideband) In certain application, a dSB modulation technique takes too much bandwidth for the channel and an ssB technique is too expensive to implement, although it takes e only half the bandwidth. In this case, a compromise between DSB and ssB, called vestigial sideband(vsB), is often chosen VSB is obtained by partial suppression of one of the sidebands of a DSB signal. sideband of the dsB signal is attenuated by using a band- pass filter, called a vestigial sideband filter. The vSB signal is given by SsB()=S(1)*h1( e Where s(t) is a dSB signal, and h,(t) is the impulse response of the VSB filter. The spectrum of the vsB signal is: ISB()=S()H1(/
25 5.5Asymmetric sideband signals (Vestigial sideband) • In certain application, a DSB modulation technique takes too much bandwidth for the channel, and an SSB technique is too expensive to implement, although it takes only half the bandwidth. In this case, a compromise between DSB and SSB, called vestigial sideband(VSB), is often chosen. • VSB is obtained by partial suppression of one of the sidebands of a DSB signal. • sideband of the DSB signal is attenuated by using a bandpass filter,called a vestigial sideband filter. The VSB signal is given by: s (t) s(t) * h (t) VSB = v • Where s(t) is a DSB signal,and hv (t) is the impulse response of the VSB filter.The spectrum of the VSB signal is : ( ) ( ) (f ) Hv f S f VSB S =