Post on 18-Nov-2014
description
TELE3113 Analogue and DigitalCommunications
VSB Modulation
Wei Zhang
w.zhang@unsw.edu.au
School of Electrical Engineering and Telecommunications
The University of New South Wales
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 SSB
and DSB-SC in the spectra characteristics is needed.
TELE3113 - VSB Modulation. August 12, 2009. – p.1/9
VSB
Instead of completely removing a sideband, a vestige of that
sideband 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.2/9
VSB Modulator
Product modulator
Carrier wave
VSB-shaping filter: )( fH
Message signal )(tm VSB-Modulated
wave )(ts
)2cos( tfA cc π
To ensure the recovery of the message signal in the
demodulation, the sideband shaping filter must satisfy:
H(f + fc) + H(f − fc) = 1, for − W ≤ f ≤ W
TELE3113 - VSB Modulation. August 12, 2009. – p.3/9
Sinusoidal VSB (1)
Consider the VSB modulation of the single-tone message
signal m(t) = Am cos(2πfmt). Let the upper and lower
side-frequencies be attenuated by the factor k and (1 − k),
respectively. The VSB spectrum is therefore,
S(f) =kAmAc
4[δ(f − fc − fm) + δ(f + fc + fm)]
+(1 − k)AmAc
4[δ(f − fc + fm) + δ(f + fc − fm)].
k = 1
2, S(f) reduces to the DSB-SC spectrum
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.4/9
Sinusoidal VSB (2)
From the spectrum S(f), we can get the VSB modulated wave,
s(t) =AmAc
4k[exp(j2π(fc + fm)t) + exp(−j2π(fc + fm)t)]
+AmAc
4(1 − k)[exp(j2π(fc − fm)t) + exp(−j2π(fc − fm)t)]
It can be further expressed as
s(t) =AmAc
2cos(2πfct) cos(2πfmt)
+AmAc
2(1 − 2k) sin(2πfct) sin(2πfmt)
TELE3113 - VSB Modulation. August 12, 2009. – p.5/9
Demodulation of VSB (1)
Product modulator
Local oscillator
Low-pass filter
Modulated wave )(ts )(tv
Demodulated signal )(tvo
)2cos(' φπ +tfAcc
It applies equally well to the demodulation of DSB-SC, SSB
and VSB.
Suppose that the local oscillator can provide the samefrequency as the carrier frequency in the modulator and a
phase difference φ equal to zero.TELE3113 - VSB Modulation. August 12, 2009. – p.6/9
Demodulation of VSB (2)
The output of the product modulator is given by
v(t) = A′
cs(t) cos(2πfct)
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
V (f) =A
′
c
2[S(f − fc) + S(f + fc)]. (1)
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(2πfct)]H(f)
where F [·] denotes the FT operator.
Suppose m(t) ⇔ M(f). Then,
F [m(t)Ac cos(2πfct)] =Ac
2[M(f − fc) + M(f + fc)].
Therefore,
S(f) =Ac
2[M(f − fc) + M(f + fc)]H(f).
TELE3113 - VSB Modulation. August 12, 2009. – p.8/9
Demodulation of VSB (4)
Shifting the VSB spectrum S(f) by ±fc, we obtain
S(f − fc) =Ac
2[M(f − 2fc) + M(f)]H(f − fc)
S(f + fc) =Ac
2[M(f) + M(f + 2fc)]H(f + fc)
Then, V (f) in equation (1) reduces to
V (f) =AcA
′
c
4M(f)
+AcA
′
c
4[M(f − 2fc)H(f − fc) + M(f + 2fc)H(f + fc)].
After passing v(t) through LPF, we get vo(t) = AcA′
c
4m(t).
TELE3113 - VSB Modulation. August 12, 2009. – p.9/9