Multiplication/Modulation Property For Continuous-Time.

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1 Multipliation/Modulation Property For Continuous-Time. X( X(j) y(=(.( Y(j)=[C(j) X(j)]/2π )] ( )* ( [ 2 ) ( ). (. π j X j C t t T F X ( C(j) + = = = θ θ θ θ θ π d Xj j C jw Y ) ( ) ( 2 ) (

2 Multipliation/Modulation Property For Disrete-time [ n]. [ n] [n] C() [n] X() F. T X 2 π [ C( j )* X ( y[n]=[n].[n] Y(j)=[C(j) X(j)]/2π j )] Y ( jw) = C( jθ ). Xj( θ ) dθ 2π 2 π 2

3 Communiation Systems Blok Diagram of AM Carrier ( ( Modulating signal ( F. T (. ( [ X ( )* C( )] 2π pulse arrier sinusoidal arrier ( e + θ ) omple eponential = = os( t j( t+ θ ) = os( t arrier + θ ) + Modulated output y( j sin( t + θ ) 3

4 Sinusoidal Amplitude Modulation with a sinusoidal arrier Modulating signal Carrier signal Modulated signal 4

5 Amplitude Modulation 5

6 Amplitude Modulation 6

7 Amplitude Modulation With Comple Eponential Carrier We h oose, arrier The frequeny is The modulated signal is : - refered to as From the multipliation property of F. T (. ( [ X ( j)* C( j)] 2π Y ( ) = X ( jθ ) C( j( θ ) dθ 2π To get bak the original signal (, ( demodulation) multiply y( with e signal For onveniene, let θ = j t. 0, ( = e y( = j( t+ θ ) the arrier frequeny. (.( F.T. = (e j t. 7

8 Amplitude Modulation and Synhronous Demodulation using omple eponential arrier. e j t ( y( e j t y( ( 8

9 Spetra assoiated with AM with omple eponential arrier Modulation F. T ( (. ( X ( ) F. T X () [ X ( )* C( )] 2π Y () Synhronous Demodulation FT Y( ) y( M M M + M ( = e j( t+ θ ) F. T C( ) C() j 2πe θ 2π j e θ C() F. T C( ) e j( t+ θ ) F. T y( Y ( ) Y () M + M M X () FT X ( ) ( M 9

10 Representation of AM with a omple eponential arrier in terms of amplitude modulation with two sinusoidal arriers with 90 0 phase differene. arrier signal Modulating signal ( e j ( t +θ ) Modulated output y( os( + θ ) t Re{y(} ( sin( + θ ) t IM{y(} 0

11 F. T ( F. T y( M X () Y () M M + M F. T Re{ y( } /2 * [ Y ( ) +Y ( )] 2 F. T Im{ y( } /2 * [ Y ( ) Y ( )] 2

12 F. T ( X ( j) M M ( = F. T os( C( j) = π[ δ ( ) + δ ( + )] π π C( j) FT y( Y ( j) = [ X ( j)* C( j)] 2π Y ( j) /2 M + M M + M 2

13 /2 Y ( j) y( = w( = os 2 w( = ( os t, y( os t t = ( + M modulation. = ( os os 2t, 2 ( os 2t 2 2 t, π + M synhronous M demodulation. π + M C( j) W ( j) /2 /4 /4 2 M M M M 2 M M 3

14 Amplitude Modulation and Synhronous Demodulation using sinusoidal arrier. os( t + θ ) ( os( t + θ ) y( Ideal lowpass filter y( w( 0 H ( j) 2 ( 0 4

15 5 Amplitude Modulation and Synhronous Demodulation using omple eponential arrier. Problem for modulator and demodulator not synhronous in phase. ( ) ( t j e +θ y( y( ) ( t j e +φ ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( t e t e e t y e w t j t j t j t j φ θ θ φ φ = = =

16 Asynhronous Demodulation need ( to be positive all the time. To use envelope detetor for demodulation, we add A to (. If K is the maimum amplitude of (, i.e. ( <=K, we require A>K, in order to make ( positive. Modulation Inde m=k/a. 6

17 Asynhronous Amplitude Modulation using sinusoidal arrier. os( A ( + y( = [ A + ( ]os t Y (w) 7

18 8

19 Advantages Synhronous Modulation/Demodulation Effiient No wastage of power sine no arrier signal being transmitted. Good for satellite ommuniations. Asynhronous Modulation/Demodulation Simple and heap iruitry at the reeiver end for the publi. 9

20 Disadvantages Synhronous Modulation/Demodulation Diffiulty of getting eat arrier frequeny at the demodulator end. Diffiulty of getting the phase at the demodulator end to be synhronous with the phase of transmitted arrier. Elaborate and epensive iruitry needed. Asynhronous Modulation/Demodulation Wastage of power sine need to transmit the arrier power whih represent no information ontent. Ineffiient. 20

21 Use of Amplitude Modulation with omple eponential arrier to implement bandpass filter with lowpass filter ( e j t y( Ideal lowpass filter H () w( 0 0 e j t f( 2

22 X() Y()W() F()

23 Frequeny-Division Multipeing 23

24 Frequeny-Division Multipeing 24

25 Frequeny-Division Multipeing 25

26 Single-Sideband Sinusoidal Amplitude Modulation 26

27 ( os t y ( t ) + Phase Shifting Proedure For Obtaining Single-sideband Signal y( H ( j) = j, > 0 = + j, < 0 p ( sin t y 2 ( p ( j) 27

28 28

29 Other Types of Modulations AM with Pulse-Train Carrier Phase Modulation. Frequeny Modulation. Pulse Amplitude Modulation. Pulse Code Modulation. (PCM). 29

30 2Hz Sinusoidal Phase Modulation with sinusoidal arrier of 00Hz. 30

31 Square Wave Phase Modulation of Sinusoidal Signal of 00Hz. 3

32 Frequeny Modulation 32

ENSC327 Communications Systems 4. Double Sideband Modulation. Jie Liang School of Engineering Science Simon Fraser University

ENSC327 Communications Systems 4. Double Sideband Modulation. Jie Liang School of Engineering Science Simon Fraser University ENSC327 Communiations Systems 4. Double Sideband Modulation Jie Liang Shool of Engineering Siene Simon Fraser University 1 Outline DSB: Modulator Spetrum Coherent Demodulator: Three methods Quadrature-arrier