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

33 demodulation of dsb sc e t m et cos 2 wet 1 met

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Unformatted text preview: r each receiver, s ubstantial c omplexity in t he receiver system c an b e j ustified, provided t here is a l arge e nough saving in expensive high-power t ransmitting e quipment. O n t he o ther h and, for a b roadcast s ystem w ith a m ultitude o f receivers for each t ransmitter, i t is m ore economical t o have one expensive high-power t ransmitter a nd s impler, less expensive receivers. T he s econd o ption ( transmitting a c arrier along w ith t he m odulated signal) is t he obvious choice in this case. T his is t he so-called A M ( amplitude m odulation), in which t he t ransmitted signal 'PAM(t) is given by 'PAM(t) = A cos wet = [A + m (t) cos wet + m (t)] cos wet (4.73a) (4.73b) Recall t hat t he DSB-SC s ignal is m (t) cos wet. F rom Eq. (4.73b) i t follows t hat t he AM signal is identical t o t he D SB-SC signal w ith A + m (t) a s t he m odulating s ignal [instead of m (t)]. T herefore, t o s ketch 'PAM (t), we sketch A + m (t) a nd - [A + m(t)] a nd fill in between w ith t he sinusoid o f t he c arrier frequency. Two cases a re c onsidered in Fig. 4.34. I n t he first case, A is large enough so t hat A + m (t) ~ 0 (is nonnegative) for all values of t. I n t he s econd case, A is n ot l arge enough t o s atisfy t his c ondition. I n t he first case, t he envelope (Fig. 4.34d) has t he s ame s hape a s m (t) ( although r iding o n a dc of m agnitude A). I n t he s econd case t he envelope s hape is n ot m (t), for some p arts g et rectified (Fig. 4.34e). T hus, we can detect t he d esired signal m (t) b y detecting t he envelope in the first case. I n t he s econd case, such a d etection is n ot possible. We shall see t hat t he envelope detection is ~ 0 f or all t !... ~ t~ 4 .7-2 283 ~ ( c) ( d) F ig. 4 .34 (e) AM signal and its envelope. an extremely simple a nd i nexpensive o peration, which does not require generation of a local carrier for t he d emodulation. B ut a s seen above t he envelope of AM has t he i nformation a bout m (t) o nly if t he AM signal [A + m (t)] cos wet satisfies t he c ondition A + m (t) > 0 for all t. Thus, t he c ondition for envelope detection of a n AM signal is A + m(t) ~ 0 for all t (4.74) I f m p is t he p eak a mplitude (positive or negative) of m (t) (see Fig. 4.34), t hen m (t) ~ - m p . Hence, t he c ondition (4.74) is equivalent t ot (4.75) T hus t he m inimum carrier a mplitude r equired for t he v iability of envelope detection is m p. T his p oint is clearly illustrated in Fig. 4.34. We define t he m odulation i ndex /1 a s /1 = mp A tIn case the negative and the positive peak amplitudes are not identical, is the absolute negative peak amplitude. (4.76) mp in condition (4.75) 4 Continuous-Time Signal Analysis: T he Fourier Transform 284 4.7 Application to Communications: Amplitude Modulation 285 where A is t he c arrier amplitude. Note t hat m p is a c onstant of t he signal m (t). Because A 2: m p a nd because there is no upper bound on A , i t follows t hat + (4.77) as the r equired condition for t...
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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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