This document discusses vestigial sideband (VSB) modulation, which is a modulation technique that lies between single sideband (SSB) and double sideband suppressed carrier (DSB-SC). VSB modulation involves transmitting a vestige, or portion, of the sideband to reduce bandwidth usage compared to DSB-SC. The key aspects covered are: 1) VSB modulation achieves a transmission bandwidth of BW + fv, where fv is the vestige bandwidth which is typically 25% of the message bandwidth BW. 2) A VSB modulator uses a product modulator and VSB shaping filter to generate the modulated signal. 3) VSB demodulation involves product

1. TELE3113 Analogue and Digital
Communications
VSB Modulation
Wei Zhang
w.zhang@unsw.edu.au
School 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 SSB
and DSB-SC in the spectra characteristics is needed.
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3. 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/

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 wave
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/

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
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6. Sinusoidal VSB (2)
From the spectrum S(f ), we can get the VSB modulated wave,
Am Ac
s(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)]
4
It 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
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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.
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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
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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).
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