5.3 Double-sideband Suppressed Carrier a double-sideband suppressed carrier(dsB-SC) signal is an AM signal that has a suppressed discrete carrier. s(t=A m(t/ t The voltage spectrum of the dsB-sC signal is S(=1/2/G(f-f)+G*f+fo)/ The percent of modulation of a DsB-sc is infinite The modulation efficiency of a DsB-sC is 100%0 A product detector(which is more expensive than an Envelope detector) is required for demodulation of the DSB-SC Signal that of a comparable am signal with the some peaf in The sideband power of a dsb-sc signal is four time level, that is to say, the DSB-SC signal has a four fold power advantage over that of an AM signal 16
16 5.3 Double-sideband Suppressed Carrier • A double-sideband suppressed carrier(DSB-SC) signal is an AM signal that has a suppressed discrete carrier. s(t) A m(t) t c c = cos • The voltage spectrum of the DSB-SC signal is S(f) 1/ 2[G(f- f ) G*(f f )] = c + + c • The percent of modulation of a DSB-SC is :infinite • The modulation efficiency of a DSB-SC is 100% • A product detector (which is more expensive than an • Envelope detector) is required for demodulation of the DSB-SC signal • The sideband power of a DSB-SC signal is four times that of a comparable AM signal with the some peak level,that is to say,the DSB-SC signal has a four_fold power advantage over that of an AM signal
5.3 Double-sideband Suppressed Carrier M(琐 B 0 B a)Magnitude spectrum of modulation Weight=Ac/2 S(琐) Weight=Ac/2 c/2 low pper sideband SIdeband f c-B -f -f+B fC-B￡￡+B b) Magnitude spectrum of AM signal Spectrum of DsB-CS signal 17
17 5.3 Double-sideband Suppressed Carrier -B 0 B f |M(f)| -fc-B -fc -fc+ B f Ac/ 2 fc-B fc fc+ B Weight=Ac/ 2 |S(f)| Weight=Ac/ 2 a) Magnitude spectrum of modulation b) Magnitude spectrum of AM signal Upper sideband low sideband Spectrum of DSB-CS signal
5.aSymmetric sideband signals (Signal sideband) An upper single sideband (UssB) signal has a zero valued spectrum forf<, where fs is the carrier frequency A lower signal sideband (LsSB)signal has a zero valued spectrum for ff where f is the carrier frequency .. SSB-AM: The bandwidth is the same as that ofthe modulating signal(which is half the bandwidth of an AM or dsB-sC signal) The term Ssb refers to the ssb-aM type of signal unless otherwise denoted 18
18 5.5Asymmetric sideband signals (Signal sideband) • An upper single sideband (USSB) signal has a zerovalued spectrum for|f|<fc ,where fc is the carrier frequency. • A lower signal sideband (LSSB) signal has a zerovalued spectrum for |f|>fc, where fc is the carrier frequency. • SSB-AM:The bandwidth is the same as that of the modulating signal (which is half the bandwidth of an AM or DSB-SC signal). • The term SSB refers to the SSB-AM type of signal , unless otherwise denoted
5.aSymmetric sideband signals Theorem: The complex envelope of an SSB signal is gIven by g(1)=A2[m(t)±jm(t) Which results in the ssb signal waveform s(t)=Am(t)cosoct + m(t)sin@t Where the upper( sign is used for USSB and the lower(+) sign is used for LssB. m(t)Denotes the Hilbert transform of m(t), which is given by: ()=m(t)*h(t) .. Where h(t=1/(t), and H(f=h(t) corresponds to a 90 phase-shift network: 0 H(O)= J f<0 19
19 5.5Asymmetric sideband signals • Theorem:The complex envelope of an SSB signal is given by g(t) A [m(t) jm ˆ(t)] = c • Which results in the SSB signal waveform: s(t) A [m(t)cos t m ˆ(t)sin t] = c c c • Where the upper(-) sign is used for USSB and the lower (+) sign is used for LSSB. Denotes the Hilbert transform of m(t), which is given by: m ˆ(t) m ˆ(t) = m(t) h(t) • Where h(t)=1/(πt), and H(f)=F[h(t)] corresponds to a • -900 phase-shift network： − = 0 0 ( ) j f j f H f
5.aSymmetric sideband signals Proof: Taking the Fouriertransform IM(fI of the complex envelope of an SsB signal, we get: B G(=A2{M(±jF[m(t)} (a) Baseband Magnitude S pectrum G(圳 Because of hilbert transform we can find that the equation becomes: G(=AMO[±jH(O 2Ac For USSB case, choose the upper sigi B th nen 2A M()f>o()Magnitude of corresponding Spectrum G()=AM(1-jH(= 0 f<0 IS(l Substituting it into eq (4-15), we have AM(-Nof>f S(∫) E-B -f f<f (b) Magnitude of corresponding Spectrum ofUssB signal f>-f Fig 5-4 Spectrum for a USSB signal 20 AcM(+fo) f<-fo
20 5.5Asymmetric sideband signals Fig.5-4 Spectrum for a USSB signal |M(f)| -B B 1 (a) Baseband Magnitude Spectrum |G(f)| -B B 2Ac (b) Magnitude of corresponding Spectrum of the complex Envelope for USSB |S(f)| -fc-B -fc fc fc+ B Ac (b) Magnitude of corresponding Spectrum of USSB signal • Proof: Taking the Fourier transform of the complex envelope of an SSB signal, we get: G( f ) A {M( f ) j [m ˆ(t)]} = c F • Because of Hilbert transform, we can find that the equation becomes: G( f ) A M( f )[1 jH( f )] = c • For USSB case, choose the upper sign, then: = − = 0 0 0 2 ( ) ( ) ( )[1 ( )] f A M f f G f A M f j H f c c • Substituting it into eq.(4-15), we have: − − + + − = c c c c c c c c f f f f A M f f f f A M f f f f S f ( ) 0 0 ( ) ( )