Communication Systems Lecture 7. Dong In Kim School of Info/Comm Engineering Sungkyunkwan University

Size: px

Start display at page:

Download "Communication Systems Lecture 7. Dong In Kim School of Info/Comm Engineering Sungkyunkwan University"

Beatrix Snow
5 years ago
Views:

1 Communiation Systems Leture 7 Dong In Kim Shool o Ino/Comm Engineering Sungkyunkwan University 1

2 Outline Expression o SSB signals Waveorm o SSB signals Modulators or SSB: Frequeny disrimination Phase disrimination Coherent Detetion o SSB 2

3 Expression o SSB Signals The DSB signal is: Its FT is: The USB signal is: s usb Proo: ( t) = A ( t) = 2 S dsb A m( t)os ( 2π t) A S ) = + 2 [ M ( ) + M ( )] ( [ m( t)os( 2π t) mˆ ( t)sin( 2π t) ] M() 1 USB() It is easier to prove in requeny domain. Shiting M() to get SSB: Reall the deinitions o pre-envelopes or analyti signals Mp() and Mn(): - 3

4 Expression o the SSB The USB signal an be written in terms o Mp() and Mn() as: Taking IFT, mˆ ( t) Next, we write mp(t) and mn(t) in terms o m(t) and : M p ( ) = M ( ) + sgn( ) M ( ) M n ( ) = M ( ) sgn( ) M ( ) 4

5 Expression o the SSB s Similarly, LSB signal an be written as: lsb A ( t) = + 2 Proo: Shiting: ( m( t)os( 2π t) mˆ ( t)sin( 2π t) ) - M() 1 LSB() 5

6 Expression o the SSB As a summary, a uniied expression o both USB and LSB is given by s ssb A ( t) = m 2 The minus sign gives USB. The plus sign gives LSB. ( m( t)os( 2π t) mˆ ( t)sin( 2π t) ) 6

7 Outline Expression o SSB signals Waveorm o SSB signals Modulators or SSB: Frequeny disrimination Phase disrimination Coherent Detetion o SSB 7

8 Waveorm o SSB Signals Reall: DSB and AM only aets the amplitude o the arrier. However, SSB hanges both amplitude and phase o the arrier! Proo: 8

9 Example Find the SSB waveorm or Solution: ( 2π t) 0.4 os( 4π t) os( t) m( t) = os 0 0 6π 0 9

10 SSB in the Time Domain m() t USB ˆm () t R(t) LSB 10

11 Outline Expression o SSB signals Waveorm o SSB signals Modulators or SSB: Method 1: requeny domain approah: Frequeny disrimination Method 2: time domain approah: Phase disrimination Coherent Detetion o SSB 11

12 Generation o SSB by Frequeny Disrimination Method 1: Generate DSB irst, then ilter out unneessary sideband: DSB M() or Filter or USB: Filter or LSB: Problems: 12

13 Phase Disrimination Modulation or SSB Method 2: Implement the time-domain expression: A sssb( t) = m 2 Need to implement Hilbert transorm ( m( t)os( 2π t) mˆ ( t)sin( 2π t) ) Only need near-ideal ilter around =0: Easier than ideal ilter around (variable) 13

14 Outline Expression o SSB signals Waveorm o SSB signals Modulators or SSB: Frequeny disrimination Phase disrimination Coherent Detetion o SSB 14

15 Coherent Detetion o SSB SSB is similar to QAM that we studied beore: s( t) = A m1 ( t)os(2π t) + A m2( t)sin(2πt ) The oherent detetion is still appliable to SSB: multiply with arrier, then LPF Assume demodulation arrier has a phase error: A ' os(2π t+ φ) 15

16 Coherent Detetion o SSB Ater LPF: A ' os(2π t+ φ) So phase error will ause some deoding distortions. I φ = 0 : ( t) y D = 16

17 Envelope Detetion o SSB Carrier reinsertion K t is loal arrier os From pilot tone or osillator e( t) K os A [ ( )os( ) ˆ t m t t m( t)sin( t)] 2 K A A m( t) os ˆ t m( t)sin( t) 2 2 I K large enough, e(t) K A m( t) os t. 2 whih is a standard AM signal an use an envelope detetor A Envelope y D(t) K m( t). 2 This method is not eiient 16-1

Summary o SSB Advantage: More bandwidth-eiient than DSB Disadvantages: Cannot be used in signals with DC (Need near-ideal ilters to avoid distortion) Solution: Vestigial sideband modulation (VSB)

18 Summary o SSB Advantage: More bandwidth-eiient than DSB Disadvantages: Cannot be used in signals with DC (Need near-ideal ilters to avoid distortion) Solution: Vestigial sideband modulation (VSB) Send one sideband plus a small part o the other sideband Ahieved by a ilter ater the DSB signal The ilter an be designed so that the message an still be reovered by the oherent DSB demodulator. Used in TV modulation. X() X() - M() S() - H() - S() 17

19 Vestigial Sideband (VSB) VSB sends a small portion o the other sideband around Bandwidth is slightly more than SSB The implementation is muh simpler than SSB Can be used in signals with DC, e.g., TV mt DSB Modulator xt H v xvsb t VSB ilter (BP) 18

20 Hv ont mt DSB Modulator xt xvsb t VSB modulation DSB X VSB ilter Hv VSB output XVSB X ( ) [ M ( ) M ( )] H ( ) 1 VSB 2 v How to design VSB ilter so that we an reover m(t)? 19

21 xvsb t dt yd t VSB Demodulation 2os wt Coherent demodulation: Multiply by arrier X ( ) [ M ( ) M ( )] H ( ) 1 VSB 2 v D( ) XVSB ( ) XVSB ( ) 1 1 [ M ( 2 ) M ( )] H( ) [ M ( ) M ( 2 )] H( ) 2 2 Ater low pass ilter 1 1 YD ( ) [ M ( )] H( ) [ M ] H( ) 2 2 M( ) [ H ( ) H ( )] 2 So i [ H( ) H( )] onstant, m(t) an be reovered. 20

22 Condition on VSB Filter [ H( ) H( )] onstant H() is anti-symmetri around 21

23 VSB Demodulation 2 Carrier reinsertion and envelope detetor an still be used or VSB m( t) os 1t 0.4os 2 1t 0.9os3 1t 22

24 VSB Demodulation 2 Message VSB output Ater arrier reinsertion K os t x ( t) r The message an be reovered rom the envelope 23

25 Summary o Linear Modulation Sheme Modulator Complexity Demodulator Complexity Power Eiieny Bandwidth DSB-SC Simple Complex (oherent) 1 2W AM Simple Simple (envelope detetor) <= 1/3 (single tone) 2W SSB Complex Coherent: omplex Envelope: simple 1: w/o arrier Low: with arrier W VSB Simpler than SSB Coherent: omplex Envelope: simple 1: w/o arrier Low: with arrier W + WVSB W WVSB: width o the vestigial sideband. WVSB 24

Dr. Md. Farhad Hossain Associate Professor Department of EEE, BUET

Dr. Md. Farhad Hossain Associate Professor Department of EEE, BUET EEE 309 Communiation Theory Semester: January 06 Dr. Md. Farhad Hossain Assoiate Proessor Department o EEE, BUET Email: marhadhossain@eee.buet.a.bd Oie: ECE 33, ECE Building Part 03-3 Single-sideband Suppressed