6.003: Signals and Systems Lecture 24 December 6, 2011

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1 6.3: Signals and Sysems Lecure 24 December 6, 2 6.3: Signals and Sysems Modulaion Subjec Evaluaions Your feedbac is imporan o us! Please give feedbac o he saff and fuure 6.3 sudens: hp://web.mi.edu/subjecevaluaion Evaluaions are open unil Friday, December 6, a noon. You will be able o view quaniaive resuls a hp://web.mi.edu/subjecevaluaion/resuls.hml and suden-wrien summaries a hp://hn.mi.edu/ug sel.php December 6, 2 Communicaions Sysems Signals are no always well mached o he media hrough which we wish o ransmi hem. Ampliude Modulaion Ampliude modulaion can be used o mach audio frequencies o radio frequencies. I allows parallel ransmission of muliple channels. signal applicaions audio video elephone, radio, phonograph, CD, cell phone, MP3 elevision, cinema, HDTV, DVD x () z () inerne coax, wised pair, cable TV, DSL, opical fiber, E/M cos w Modulaion can improve mach based on frequency. x 2 () z 2 () z() LPF y() cos w 2 cos w c x 3 () z 3 () cos w 3 Superheerodyne Receiver Edwin Howard Armsrong invened he superheerodyne receiver, which made broadcas AM pracical. Ampliude, Phase, and Frequency Modulaion There are many ways o embed a message in a carrier. Ampliude Modulaion (AM) + carrier: y () = ( x() + C ) cos( ) Phase Modulaion (PM): Frequency Modulaion (FM): y 2 () = cos( + x()) ( y 3 () = cos + ) x(τ)dτ PM: signal modulaes insananeous phase of he carrier. y 2 () = cos( + x()) Edwin Howard Armsrong also invened and paened he regeneraive (posiive feedbac) circui for amplifying radio signals (while he was a junior a Columbia Universiy). He also invened wide-band FM. FM: signal modulaes insananeous frequency of carrier. ( ) y 3 () = cos + x(τ)dτ } {{ } φ() ω i () = + d d φ() = + x()

2 6.3: Signals and Sysems Lecure 24 December 6, 2 Frequency Modulaion Compare AM o FM for x() = cos( ). AM: y () = ( x() + C ) cos( ) = (cos( ) +.) cos( ) FM: y 3 () = cos ( + x(τ)dτ) = cos( + sin( )) Frequency Modulaion Early invesigaors hough ha narrowband FM could have arbirarily narrow bandwidh, allowing more channels han AM. ( ) y 3 () = cos + x(τ)dτ } {{ } φ() ω i () = + d d φ() = + x() Small small bandwidh. Righ? Advanages of FM: consan power no need o ransmi carrier (unless DC imporan) bandwidh? Frequency Modulaion Early invesigaors hough ha narrowband FM could have arbirarily narrow bandwidh, allowing more channels han AM. Wrong! ( y 3 () = cos + = cos( ) cos ( ) x(τ)dτ If ( hen ) cos x(τ)dτ ( ) sin x(τ)dτ x(τ)dτ ( ) y 3 () cos( ) sin( ) x(τ)dτ ) ( ) x(τ)dτ sin( ) sin x(τ)dτ Bandwidh of narrowband FM is he same as ha of AM! (inegraion does no change he highes frequency in he signal) Phase/Frequency Modulaion Find he Fourier ransform of a PM/FM signal. y() = cos( + mx()) = cos( + m sin( )) = cos( ) cos(m sin( ))) sin( ) sin(m sin( ))) x() is periodic in T = 2π, herefore cos(m sin( )) is periodic in T. m sin( ) m m cos(m sin( )) increasing m Phase/Frequency Modulaion Find he Fourier ransform of a PM/FM signal. y() = cos( + mx()) = cos( + m sin( )) = cos( ) cos(m sin( ))) sin( ) sin(m sin( ))) x() is periodic in T = 2π, herefore cos(m sin( )) is periodic in T. cos(m sin( )) Phase/Frequency Modulaion Find he Fourier ransform of a PM/FM signal. y() = cos( + mx()) = cos( + m sin( )) = cos( ) cos(m sin( ))) sin( ) sin(m sin( ))) x() is periodic in T = 2π, herefore cos(m sin( )) is periodic in T. cos(m sin( )) m = 5 m = 5 a a

3 6.3: Signals and Sysems Lecure 24 December 6, 2 Phase/Frequency Modulaion Fourier ransform of firs par. x() = sin( ) y() = cos( + mx()) = cos( + m sin( )) = cos( ) cos(m sin( ))) sin(ω }{{} c ) sin(m sin( ))) ya() Y a (jω) m = 5 Phase/Frequency Modulaion Find he Fourier ransform of a PM/FM signal. y() = cos( + mx()) = cos( + m sin( )) = cos( ) cos(m sin( ))) sin( ) sin(m sin( ))) x() is periodic in T = 2π, herefore sin(m sin( )) is periodic in T. m sin( ) m ωm ω m sin(m sin( )) increasing m increasing m Phase/Frequency Modulaion Find he Fourier ransform of a PM/FM signal. y() = cos( + mx()) = cos( + m sin( )) = cos( ) cos(m sin( ))) sin( ) sin(m sin( ))) x() is periodic in T = 2π, herefore sin(m sin( )) is periodic in T. sin(m sin( )) Phase/Frequency Modulaion Find he Fourier ransform of a PM/FM signal. y() = cos( + mx()) = cos( + m sin( )) = cos( ) cos(m sin( ))) sin( ) sin(m sin( ))) x() is periodic in T = 2π, herefore sin(m sin( )) is periodic in T. sin(m sin( )) m = 5 m = 5 b b Phase/Frequency Modulaion Fourier ransform. x() = sin( ) y() = cos( + mx()) = cos( + m sin( )) = cos( ) cos(m sin( ))) sin(ω }{{} c ) sin(m sin( ))) }{{} ya() y b () Frequency Modulaion Wideband FM is useful because i is robus o noise. AM: y () = (cos( ) +.) cos( ) Y (jω) m = 5 FM: y 3 () = cos( + m sin( )) ω ωm FM generaes a redundan signal ha is resilien o addiive noise. 3

4 6.3: Signals and Sysems Lecure 24 December 6, Microscopy 6.3 Model of a Microscope microscope Dennis M. Freeman Sanley S. Hong Jewan Ryu Michael S. Mermelsein Berhold K. P. Horn Microscope = low-pass filer Phase-Modulaed Microscopy microscope 4

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