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