Part 5 – Communication theory – Vestigial side band modulation

In single side band modulation, one of the methods of modulations was frequency discrimination method. But it wasn’t a effective for SSB modulation because it also let in some parts of side band we didn’t want to be modulated. As a solution, only message signals which didn’t have very low frequencies could be effectively SSB modulated. But this meant video signals and computer data couldn’t be SSB modulated. Vestigial side band modulation is the answer to this problem.

Under Vestigial side band modulation, we don’t completely remove one side band but rather purposefully allow a trace or a vestige of that side band to be transmitted.

Bandwidth=W+f_v (f_v is the vestige bandwidth)

Modulation:

The side band shaping filter is a band pass filter. It is a practical band pass filter. It’s cut off frequency is not exactly f_c. Hence we don’t completely remove one side band but rather allow a trace of it to be transmitted. This is done purposefully.

Transfer function of the band pass filter:

where u(f) is a unit step response and H_v(f) is the frequency response of the low pass filter.

The filter shown below is used to build a vestigial lower side band modulated signal (lower side is the vestigial part)

c. The function in figure (a) shifted by frequency fc

b. frequency response of a low pass filter.Note the odd symmetry around the frequency 0.

The function in figure (b) shifted by frequency fc. Note the odd symmetry around the frequency fc.

The transfer function of the band pass filter. Only the part highlighted in blue is significant.It must have odd symmetry above the carrier frequency and relative response of 0.5 at fc . After fc+W, the transfer function is arbitrary.

The part of the frequency response from ( f_c-f_v ) to f_c lets the trace of the lower side band to transmitted along with the upper side band.

Demodulation:

As in the case of DSB – SC (double side band suppressed carrier) and SSB (single side band) modulation, we use coherent detection method for demodulation of vestigial side band modulation. Under this method, we multiply the received signal with a locally generated copy of the carrier signal. This locally generated carrier signal must maintain perfect synchronisation (with respect to frequency and phase) with the original carrier signal.

Substituting U(f-f_c) and U(f+f_c) in V(f) equation, we get,

Looking at the expression above,we can see that the first term is a scaled version of the message signal and the second term contains high frequency components. Using a low pass filter with a cut off frequency slightly above W, we can eliminate the second term, leaving us with the first term. But if the term H(f-f_c)+H(f+f_c) is not constant through the bandwidth of M(f), then the first term will be scaled but it will be a distorted version of the message signal.

Hence one of the requirements of vestigial side band modulation is that

The VSB modulation has become standard for the analogue transmission of television and
similar signals, where transmission of low-frequency components is important, but the
bandwidth required for double sideband transmission is unavailable.
In the transmission of television signals in practice, a controlled amount of carrier is added to
the VSB modulated signal. This is done to permit the use of and envelope detector for
demodulation. The design of the receiver is thereby considerably simplified.

Advantages:

It has a bandwidth of only W +f_v . Meanwhile Standard AM has a bandwidth of 2W.
Modulation and transmission of message signals containing low frequencies is possible.
Less power is needed as compared to Standard AM and DSB-SC.
Due to the allowance of transmitting a part of the lower side band, the strict constraints of the band pass filters have been relaxed. So practical and easy to design filters can be used.

Disadvantages: