Tele3113 wk4wed
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TELE3113 Analogue and DigitalCommunications
VSB Modulation
Wei Zhang
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 .
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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
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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
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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)
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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)
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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).
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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).
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