Signal Processing and Linear Systems-B.P.Lathi copy

432a shifted to the right and the left by we times

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Unformatted text preview: st i dentical t o m odulation, c onsists of m ultiplication o f t he i ncoming m odulated s ignal m et) cos wet b y a c arrier cos wet followed b y a l owpass filter, as d epicted in Fig. 4.33a. We c an verify t his c onclusion d irectly in t he t ime-domain b y o bserving t hat t he s ignal e (t) in Fig. 4.33a is 2 Hence, e (t) c onsists o f t wo c omponents ~m(t) a nd ~m(t) cos 2wct, w ith t heir s pectra, a s i llustrated in Fig. 4.33b. T he s pectrum o f t he s econd c omponent, b eing a m odulated s ignal w ith c arrier f requency 2w c, is c entered a t ± 2wc. H ence, t his c omponent is s uppressed b y t he l owpass filter i n F ig. 4.33a. T he d esired c omponent ~M(w), b eing a lowpass s pectrum ( centered a t w = 0), p asses t hrough t he filter u nharmed, r esulting i n t he o utput ~m(t). A p ossible form o f l owpass filter c haracteristics is d epicted ( dotted) i n Fig. 4.33b. T his m ethod o f r ecovering t he b aseband s ignal is called s ynchronous d etection, o r c oherent d etection, w here we use a c arrier o f e xactly t he s ame f requency ( and p hase) a s t he c arrier u sed for m odulation. T hus, for d emodulation, we n eed t o g enerate a local c arrier a t t he r eceiver i n f requency a nd p hase c oherence (synchronism) w ith t he c arrier u sed a t t he m odulator. W e s hall d emonstrate in E xample 4.18 t hat b oth, t he p hase a nd f requency synchronism, a re e xtremely c ritical. • F ig. 4 .33 Demodulation of DSB-SC. e (t) = m et) cos 2 wet 1 = - [met) + m et) cos 2wet] (4.72b) (4.72a) tThe term suppressed carrier does not necessarily mean absence of the spectrum at the carrier frequency. T he term "suppressed carrier" merely implies that there is no discrete component of the carrier frequency. Since no discrete component exists, the spectrum of DSB-SC does not have impulses at ±we, a fact which further implies t hat the modulated signal met) cos wet does not contain a term of the form k cos wet (assuming that m( t) has a zero mean value). E xample 4 .18 Discuss the effect of lack of frequency and phase coherence (synchronism) between the carriers a t t he modulator (transmitter) and the demodulator (receiver) in DSB-SC. Let the modulator carrier be cos wet (Fig. 4.31a). For the demodulator in Fig. 4.33a, we shall consider two cases: (1) the first case with carrier cos (wet + 8) (phase error of 8) and (2) the second case with carrier cos (we + il.w)t (frequency error il.w). (a) With t he demodulator carrier cos (wet + 8) (instead of cos wet) in Fig. 4.33a, the multiplier o utput is e(t) = m (t) cos wet cos (wet + 8) instead of m (t)cos 2 wet. Using the trigonometric identity, we o btain e(t) = met) cos wet cos (wet + 8) 1 = 2m(t)[cos 8 + cos (2wet + 8)] The spectrum of the component 1 m(t) cos (2wet + 8) is centered a t ±2we. Consequently, it will be filtered out by the lowpass filter a t t he output. T he component 1 m(t) cos 8 is the signal met) multiplied by a constant 1cos 8. T he s pectrum of this component is centered a t W =...
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This note was uploaded on 04/14/2013 for the course ENG 350 taught by Professor Bayliss during the Spring '13 term at Northwestern.

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