# Describe Vestigial Sideband Transmission (VSB) . Applications of Vestigial Siddeband Transmission

## Vestigial Sideband Transmission

The exact frequency response requirements on the sideband filter in SSB-SC system can be relaxed by allowing a part of the unwanted sideband called vestige to appear in the output of the modulator.

Due to this, the design of the sideband filter is simplified to a great extent .

But the bandwidth of the system is increased slightly .

To generate a VSB signal, we have to first generate a DSB-SC signal and then pass it through a sideband filter as shown in fig. 1 . This filter will pass the wanted sideband as it is along with a part of unwanted sideband .

Fig.1 : VSB Transmitter

## Frequency Domain Description

### Frequency Spectrum

The spectrum of VSB is as shown in fig. 2 .

(a) Spectrum of message signal

(b) Spectrum of VSB Signal

Fig. 2

The spectrum of message signal x(t) has also been shown .

In the frequency spectrum, it is assumed that the upper sideband is transmitted as it is and the lower sideband is modified into vestigial sideband .

### Transmission Bandwidth

From fig. 2 (b), it is evident that the transmission bandwidth of the VSB modulated wave is given by :

Where f_{m }= Message bandwidth

f_{v }= Width of the vestigial sideband

## Advantages of VSB

- The main advantage of VSB modulation is the reduction in bandwidth. It is almost as efficient as the SSB .
- Due to allowance of transmitting a part of lower sideband, the constraint on the filter have been relaxed . So practically, easy to design filters can be used .
- It possesses good phase characteristics and makes the transmission of low frequency components possible .

## Application of VSB

VSB modulation has become standard for the transmission of television signal . Because the video signal need a large transmission bandwidth if transmitted using DSB-FC or DSB-SC techniques .

## Generation of VSB Modulated Wave

The block diagram of a VSB modulator is shown in fig.3 .

Fig.3 : Generation of VSB Signal

The modulating signal x(t) is applied to a product modulator . The output of the carrier oscillator is also applied to the other input of the product modulator . The output of the product modulator is then given by :

m(t) = x(t) . c(t)

= x(t) . V_{c }cos(2π f_{c}t)

This represents a DSB-SC modulated wave .

This DSB-SC signal is then applied to a sideband shaping filter . The ddesign of this filter depends on the desired spectrum of the VSB modulated signal.

This filter will pass the wanted sideband and the vestige of the unwanted sideband .

Let the transfer function of the filter be H(f) .

Hence, the spectrum of the VSB modulated signal is given by :

## Demodulation of VSB Wave

The block diagram of the VSB demodulator is shown in fig.4 .

Fig.4 : VSB demodulator

### Working Operation

The VSB modulated wave is passed through a product modulator where it is multiplied with the locally generated synchronous carrier .

Hence, the output of the product modulator is given by :

Taking the Fourier transform of both sides, we get

But

Hence, we have

The first term in the above expression represents the VSB modulated wave, corresponding to a carrier frequency of 2f_{c .}This term will be eliminated by the filter to produce output v_{o}(t) .

The second term in the above expression for M(f) represents the spectrum of demodulated VSB output .

Therefore ,

This spectrum is shown in fig.5 .

fig 5: Spectrum of VSB Demodulator

In order to obtain the undistorted message signal x(t) at the output of the demodulator, V_{o}(f) should be a scaled version of X(f) .

For this the transfer function H(f) should satisfy the following conditions :

Where H( f_{c}) is constant .