TELE3113 Analogue and Digital      Communications               DSB-SC Modulation                      Wei Zhang          ...
DSB-SC Modulation (1) Double sideband-suppressed carrier (DSB-SC) modulation consists of the product of the message signal...
DSB-SC Modulation (2)                                  Message Signal m(t)    10     5     0    −5   −10          0   0.1 ...
DSB-SC Modulation (3)      Spectrum of message signal M ( f )                                        M (0)                ...
DSB-SC Modulation (4) The modulated signal s(t) undergoes a phase reversal whenever the message signal m(t) crosses zero. ...
Example of DSB-SC ModulationConsider DSB-SC modulation of a single-tone message signalm(t) = Am cos(2πfm t). The modulated...
Coherent Detection (1)     Modulated                                                      Demodulated     wave s (t )     ...
Coherent Detection (2)Denote the local oscillator signal by Ac cos(2πfc t + φ). Thedetector output is therefore    v(t) = ...
Coherent Detection (3)Consider the output of the product modulator,         1                           1   v(t) = Ac Ac c...
Coherent Detection (4)After the low-pass filtering the signal v(t), at the filter output weobtain                           ...
Costas Loop: carrier phase recovery                                           I-channel                                   ...
Upcoming SlideShare
Loading in …5
×

Tele3113 wk3wed

1,231 views

Published on

Published in: Education
0 Comments
0 Likes
Statistics
Notes
  • Be the first to comment

  • Be the first to like this

No Downloads
Views
Total views
1,231
On SlideShare
0
From Embeds
0
Number of Embeds
10
Actions
Shares
0
Downloads
27
Comments
0
Likes
0
Embeds 0
No embeds

No notes for slide

Tele3113 wk3wed

  1. 1. TELE3113 Analogue and Digital Communications DSB-SC Modulation Wei Zhang w.zhang@unsw.edu.auSchool of Electrical Engineering and Telecommunications The University of New South Wales
  2. 2. DSB-SC Modulation (1) Double sideband-suppressed carrier (DSB-SC) modulation consists of the product of the message signal m(t) and the carrier wave c(t), as given by s(t) = c(t)m(t) = Ac cos(2πfc t)m(t). The Fourier transform of the DSB-SC modulated signal is Ac S(f ) = [M (f − fc ) + M (f + fc )] 2 where we used the relation: m(t) exp(j2πfc t) ⇔ M (f − fc ) Shifting Property TELE3113 - DSB-SC Modulation. August 5, 2009. – p.1/1
  3. 3. DSB-SC Modulation (2) Message Signal m(t) 10 5 0 −5 −10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Carrier Wave c(t) 1 0.5 0 −0.5 −1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 DSB−SC Modulated Signal s(t) 5 0 −5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 TELE3113 - DSB-SC Modulation. August 5, 2009. – p.2/1
  4. 4. DSB-SC Modulation (3) Spectrum of message signal M ( f ) M (0) f −W 0 W Spectrum of DSB-SC modulated signal S( f ) Ac M (0) 2 Lower Upper sideband sideband − fc − W − fc − fc + W fc − W fc fc + W f 0 TELE3113 - DSB-SC Modulation. August 5, 2009. – p.3/1
  5. 5. DSB-SC Modulation (4) The modulated signal s(t) undergoes a phase reversal whenever the message signal m(t) crosses zero. The envelope of the modulated signal s(t) is different from the message signal. So the simple demodulation using an envelop detection is not an option for DSB-SC modulation. TELE3113 - DSB-SC Modulation. August 5, 2009. – p.4/1
  6. 6. Example of DSB-SC ModulationConsider DSB-SC modulation of a single-tone message signalm(t) = Am cos(2πfm t). The modulated signal is therefore givenby s(t) = Am Ac cos(2πfm t) cos(2πfc t).The FT of the DSB-SC modulated signal is given by Am Ac Am Ac S(f ) = δ(f − fc − fm ) + δ(f + fc + fm ) 4 4 Am Ac Am Ac + δ(f − fc + fm ) + δ(f + fc − fm ). 4 4 TELE3113 - DSB-SC Modulation. August 5, 2009. – p.5/1
  7. 7. Coherent Detection (1) Modulated Demodulated wave s (t ) v(t ) signal v o (t ) Product Low-pass modulator filter Ac cos(2πf c t + φ ) Local oscillatorSuppose in the receiver the local oscillator can provide thesame frequency, but arbitrary phase difference φ, measuredwith respect to the carrier wave c(t). TELE3113 - DSB-SC Modulation. August 5, 2009. – p.6/1
  8. 8. Coherent Detection (2)Denote the local oscillator signal by Ac cos(2πfc t + φ). Thedetector output is therefore v(t) = Ac cos(2πfc t + φ)s(t) = Ac Ac cos(2πfc t + φ) cos(2πfc t)m(t) 1 1 = Ac Ac cos(4πfc t + φ)m(t) + Ac Ac cos(φ)m(t), 2 2where we used the relation 1 1 cos(θ1 ) cos(θ2 ) = cos(θ1 + θ2 ) + cos(θ1 − θ2 ). 2 2 TELE3113 - DSB-SC Modulation. August 5, 2009. – p.7/1
  9. 9. Coherent Detection (3)Consider the output of the product modulator, 1 1 v(t) = Ac Ac cos(4πfc t + φ)m(t) + Ac Ac cos(φ)m(t). 2 2The Fourier transform of v(t) is given by 1 V (f ) = Ac Ac [M (f − 2fc ) + M (f + 2fc )] 4 1 + Ac Ac cos(φ)M (f ). 2The first term is a high-frequency signal centered at ±2f c and thesecond term is a low-frequency signal centered at 0. TELE3113 - DSB-SC Modulation. August 5, 2009. – p.8/1
  10. 10. Coherent Detection (4)After the low-pass filtering the signal v(t), at the filter output weobtain 1 vo (t) = Ac Ac cos(φ)m(t). 2 As long as the phase error φ is constant, the detector output provides an undistorted version of the message signal m(t). In practice, however, the phase error φ varies randomly with time, thereby causing the coherent detection difficult. Therefore, the local oscillator in the receiver must synchronize in both frequency and phase with the carrier wave c(t). TELE3113 - DSB-SC Modulation. August 5, 2009. – p.9/1
  11. 11. Costas Loop: carrier phase recovery I-channel 1 A cos(φ ) m(t ) Product Low-pass 2 c modulator filter Demodulated signal cos( 2πf c t + φ ) Voltage-controlled Phase oscillator discriminator DSB-SC wave s (t ) − 90 0 Phase-shifter sin( 2πf c t + φ ) Product Low-pass modulator filter 1 Ac sin(φ ) m(t ) 2 Q-channel TELE3113 - DSB-SC Modulation. August 5, 2009. – p.10/1

×