x(at) 1 x(t) h(t) H( jω )X( jω ) x(t)p(t) 1 X( jω ) P( jω) x(t t d ) e jωt d x(t)e jω 0t X( j(ω ω 0 )) LECTURE OBJECTIVES Signal Processing First

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Robyn Jackson
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1 Signal Proessing Firs Leure 4 Ampliude Modulaion AM LECURE OBJECIVES Review of F properies Convoluion <--> mulipliaion Frequen shifing Sinewave Ampliude Modulaion AM radio Frequen-division mulipleing FDM Reading: Chaper, Seion - 4/9/ , JH MClellan & RW Shafer 4/9/ , JH MClellan & RW Shafer 3 able of Eas F Properies Lineari Proper a b a b Dela Proper d e d Frequen Shifing Saling a a a 4/9/ , JH MClellan & RW Shafer 4 able of F Properies h H p P Differeniaion Proper d d 4/9/ , JH MClellan & RW Shafer 5

2 Frequen Shifing Proper e 0 e d e 0 d sin 7 π 4/9/ , JH MClellan & RW Shafer 6 0 e 0 7 < < elsewhere Convoluion Proper Convoluion in he ime-domain h hτ τ dτ orresponds o MULIPLICAION in he frequen-domain h H H 4/9/ , JH MClellan & RW Shafer 7 Cosine Inpu o LI Ssem H H [ 0 0 ] H 0 0 H 0 0 H 0 e 0 H 0 e 0 H 0 e 0 H * 0 e 0 H 0 os 0 H 0 4/9/ , JH MClellan & RW Shafer 8 Ideal Lowpass Filer o o H lp if 0 < o 0 if 0 > o 4/9/ , JH MClellan & RW Shafer 9

3 Ideal LPF: Fourier Series H < o 0 > o he wa ommuniaion ssems work f o "uoff freq." 4 sin 50π π 4 sin 50π 3π How do we share bandwidh? 4/9/ , JH MClellan & RW Shafer 0 4/9/ , JH MClellan & RW Shafer able of F Properies h H p P Differeniaion Proper d d 4/9/ , JH MClellan & RW Shafer Signal Muliplier Modulaor p p P Mulipliaion in he ime-domain orresponds o onvoluion in he frequen-domain. θ P θdθ 4/9/ , JH MClellan & RW Shafer 3

4 4/9/ , JH MClellan & RW Shafer 4 π P p [ ] os π os P p 4/9/ , JH MClellan & RW Shafer 5 Ampliude Modulaor modulaes he ampliude of he osine wave. he resul in he frequen-domain is wo shifed opies of. os os 4/9/ , JH MClellan & RW Shafer 6 os sin sin os sin 0 > < 4/9/ , JH MClellan & RW Shafer 7 os

5 DSBAM Modulaor DSBAM Waveform os os In he ime-domain, he envelope of sinewave peaks follows If 0 for > b and > b,he resul in he frequen-domain is wo shifed and saled ea opies of. 4/9/ , JH MClellan & RW Shafer 8 4/9/ , JH MClellan & RW Shafer 9 Double Sideband AM DSBAM DSBAM DEmodulaor pial bandlimied inpu signal os w v os os Frequen-shifed opies Lower sideband Upper sideband w [os ] os W 4 4 V H W 4/9/ , JH MClellan & RW Shafer 0 4/9/ , JH MClellan & RW Shafer

6 DSBAM Demodulaion H < o 0 > o Frequen-Division Mulipleing FDM Shifing sperum of signal o higher frequen: Permis ransmission of low-frequen signals wih high-frequen EM waves B alloaing a frequen band o eah signal muliple bandlimied signals an share he same hannel AM radio: khz 0 khz bands FM radio: MHz 00 khz bands V 4/9/005 H W 003, JH MClellan & RW Shafer if b < o < b 4/9/ , JH MClellan & RW Shafer 3 FDM Blok Diagram mier Frequen-Division De-Mu os Sperum of inpus mus be bandlimied Need > b os os os 4/9/ , JH MClellan & RW Shafer 4 4/9/ , JH MClellan & RW Shafer 5

7 Bandpass Filers for De-Mu Pop Quiz: F hru LPF H LP o o k Inpu 4 30π k If he oupu is, hen find a value for o 4/9/ , JH MClellan & RW Shafer 6 4/9/ , JH MClellan & RW Shafer 7

Example Message bandwidth and the transmitted signal bandwidth

Example Message bandwidth and the transmitted signal bandwidth 4.6 Bandwidh-Eiien Modulaions 4.74. We are now going o deine a quaniy alled he bandwidh o a signal. Unorunaely, in praie, here isn jus one deiniion o bandwidh. Deiniion 4.75. The bandwidh (BW) o a signal