Whenever you pass a signal through a low-pass filter, it does not cut the signal exactly at the transition edge. A real filter does not have an ideal stopband, so some unwanted frequency components always remain.
The same principle applies to VSB (Vestigial Sideband) modulation.
VSB is generated from a Double-Sideband Suppressed-Carrier (DSB-SC) signal. In DSB-SC, both the upper sideband (USB) and lower sideband (LSB) are present.
If we pass a DSB-SC signal through a low-pass filter in an attempt to extract only one sideband (like SSB), the filter cannot perfectly remove the unwanted sideband because practical filters have gradual roll-off.
Therefore, instead of extracting exactly one complete sideband, we keep one full sideband and allow a small portion of the other sideband to pass. This remaining portion is called the vestigial sideband.
Because of this added “vestige,” the bandwidth of VSB is slightly larger than the bandwidth of SSB-SC.
Vestigial Sideband Modulation (VSB)
Vestigial Sideband Modulation (VSB) is a form of amplitude modulation in which one sideband is transmitted completely while only a small part (vestige) of the other sideband is retained. It is commonly used in television broadcasting systems such as NTSC and PAL because it provides a trade-off between bandwidth efficiency and ease of filtering.
1. Generation of VSB
The message signal \( m(t) \) is multiplied with a carrier \( \cos(2\pi f_c t) \) to produce a double-sideband suppressed carrier (DSB-SC) signal:
$$ s_{\text{DSB}}(t) = m(t)\cos(2\pi f_c t) $$
The spectrum of this signal is:
$$ S_{\text{DSB}}(f) = \frac{1}{2}[M(f-f_c) + M(f+f_c)] $$
To convert DSB-SC into VSB, the signal is passed through a VSB filter whose frequency response \( H_{\text{VSB}}(f) \) suppresses most of one sideband while allowing a small “vestige” to remain. The resulting spectrum is:
$$ S_{\text{VSB}}(f) = S_{\text{DSB}}(f) \cdot H_{\text{VSB}}(f) $$
2. Frequency-Domain Representation
Let the upper sideband be passed completely and the lower sideband be partially attenuated. Then:
$$ S_{\text{VSB}}(f) = \frac{1}{2} M(f-f_c) + \frac{1}{2} M(f+f_c) \cdot H_{\text{VSB}}(f) $$
The vestigial portion ensures that the system maintains approximate symmetry around the carrier, which is necessary for distortion-free demodulation of low-frequency signals (important in video transmission).
3. Demodulation of VSB
Demodulation is performed using coherent detection:
$$ r(t) = s_{\text{VSB}}(t) \cdot 2\cos(2\pi f_c t) $$
In the frequency domain:
$$ R(f) = S_{\text{VSB}}(f-f_c) + S_{\text{VSB}}(f+f_c) $$
After low-pass filtering, the recovered message spectrum becomes:
$$ \hat{M}(f) = M(f)\cdot H_{\text{eq}}(f) $$
where the equivalent filter is:
$$ H_{\text{eq}}(f) = \frac{1}{2} \left[ 1 + H_{\text{VSB}}(f) \right] $$
If the vestigial filter is properly designed:
$$ H_{\text{eq}}(f) = 1 $$
ensuring distortion-free recovery.
4. Bandwidth Requirement
The bandwidth of a VSB signal is approximately:
$$ B_{\text{VSB}} = B + B_v $$
where \( B \) is the message bandwidth and \( B_v \) is the vestigial bandwidth (typically around 0.25 B in TV applications).
5. Applications of VSB
- Analogue television transmission (NTSC, PAL)
- High-quality broadcast systems with low-frequency components
- Situations needing a balance between bandwidth and simplicity
6. Advantages
- Lower bandwidth than conventional AM
- Easier filtering than SSB
- Good for signals with low-frequency content
7. Disadvantages
- More complex than AM
- Less bandwidth-efficient than pure SSB