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  • 1. TELE3113 Analogue and Digital Communications VSB Modulation Wei Zhang w.zhang@unsw.edu.auSchool of Electrical Engineering and Telecommunications The University of New South Wales
  • 2. Motivation The spectrally efficient transmission of wideband signals (e.g., TV video signals) contain significant low frequencies. SSB has a narrow BW, so it is not practical in this case. DSB-SC requires a BW equal to twice the message BW, so it is not an option.A compromise method of modulation that lies between SSBand DSB-SC in the spectra characteristics is needed. TELE3113 - VSB Modulation. August 12, 2009. – p.1/
  • 3. VSBInstead of completely removing a sideband, a vestige of thatsideband is transmitted; hence, the name “vestigial sideband”.The transmission BW of a VSB modulated signal is defined by BT = fv + W,where fv is the vestige BW and W is the message BW. Typically,fv is 25% of W . TELE3113 - VSB Modulation. August 12, 2009. – p.2/
  • 4. VSB Modulator Message signal VSB-Modulated m (t ) Product VSB-shaping wave s (t ) modulator filter: H ( f ) Ac cos( 2πf c t ) Carrier waveTo ensure the recovery of the message signal in thedemodulation, the sideband shaping filter must satisfy: H(f + fc ) + H(f − fc ) = 1, for − W ≤ f ≤ W TELE3113 - VSB Modulation. August 12, 2009. – p.3/
  • 5. Sinusoidal VSB (1) Consider the VSB modulation of the single-tone message signal m(t) = Am cos(2πfm t). Let the upper and lower side-frequencies be attenuated by the factor k and (1 − k), respectively. The VSB spectrum is therefore, kAm Ac S(f ) = [δ(f − fc − fm ) + δ(f + fc + fm )] 4 (1 − k)Am Ac + [δ(f − fc + fm ) + δ(f + fc − fm )]. 4 k = 1 , S(f ) reduces to the DSB-SC spectrum 2 k = 0, S(f ) reduces to the lower SSB spectrum k = 1, S(f ) reduces to the upper SSB spectrum TELE3113 - VSB Modulation. August 12, 2009. – p.4/
  • 6. Sinusoidal VSB (2)From the spectrum S(f ), we can get the VSB modulated wave, Am Acs(t) = k[exp(j2π(fc + fm )t) + exp(−j2π(fc + fm )t)] 4 Am Ac + (1 − k)[exp(j2π(fc − fm )t) + exp(−j2π(fc − fm )t)] 4It can be further expressed as Am Ac s(t) = cos(2πfc t) cos(2πfm t) 2 Am Ac + (1 − 2k) sin(2πfc t) sin(2πfm t) 2 TELE3113 - VSB Modulation. August 12, 2009. – p.5/
  • 7. Demodulation of VSB (1) Modulated Demodulated wave s (t ) v(t ) signal v o (t ) Product Low-pass modulator filter Ac cos(2πf c t + φ ) Local oscillator It applies equally well to the demodulation of DSB-SC, SSB and VSB. Suppose that the local oscillator can provide the same frequency as the carrier frequency in the modulator and a phase difference φ equal to zero. TELE3113 - VSB Modulation. August 12, 2009. – p.6/
  • 8. Demodulation of VSB (2) The output of the product modulator is given by v(t) = Ac s(t) cos(2πfc t) where s(t) is the VSB modulated wave. Next, we want to show how to demodulate the message signal m(t) from v(t). Suppose s(t) ⇔ S(f ). Then, the FT of the signal v(t) is given by Ac V (f ) = [S(f − fc ) + S(f + fc )]. (1) 2 TELE3113 - VSB Modulation. August 12, 2009. – p.7/
  • 9. Demodulation of VSB (3) Note that S(f ) is the spectrum of the VSB modulated signal s(t). From the block diagram of the VSB modulator, we can obtain S(f ) = F [m(t)Ac cos(2πfc t)]H(f ) where F [·] denotes the FT operator. Suppose m(t) ⇔ M (f ). Then, Ac F [m(t)Ac cos(2πfc t)] = [M (f − fc ) + M (f + fc )]. 2 Therefore, Ac S(f ) = [M (f − fc ) + M (f + fc )]H(f ). 2 TELE3113 - VSB Modulation. August 12, 2009. – p.8/
  • 10. Demodulation of VSB (4) Shifting the VSB spectrum S(f ) by ±fc , we obtain Ac S(f − fc ) = [M (f − 2fc ) + M (f )]H(f − fc ) 2 Ac S(f + fc ) = [M (f ) + M (f + 2fc )]H(f + fc ) 2 Then, V (f ) in equation (1) reduces to Ac Ac V (f ) = M (f ) 4 Ac Ac + [M (f − 2fc )H(f − fc ) + M (f + 2fc )H(f + fc )]. 4 Ac Ac After passing v(t) through LPF, we get vo (t) = 4 m(t). TELE3113 - VSB Modulation. August 12, 2009. – p.9/