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Tele3113 wk4wed

1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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/