The stringent frequency-response requirements on the sideband filter in a SSB AM system can be relaxed by allowing a part, called a vestige, of the unwanted sideband to appear at the output of the modulator.
- We simplify the design of the sideband filter at the cost of a modest increase in the channel bandwidth required to transmit the signal. The resulting signal is called vestigial-sideband (VSB) AM.
- To generate a VSB AM signal we begin by generating a DSB-SC AM signal and passing it through a sideband filter with frequency response H( f ) as shown in Figure 3.10. In the time domain the VSB signal may be expressed as
Generation of the VSB
Demodulation of the VSB
where h(t) is the impulse response of the VSB filter. In the frequency domain, the corresponding expression is
- To determine the frequency-response characteristics of the filter, let us consider the demodulation of the VSB signal u(t). We multiply u(t) by the carrier component cos 2π fct and pass the result through an ideal lowpass filter, as shown in Figure 3.11.
- Thus, the product signal is
- The low pass filter rejects the double-frequency terms and passes only the components in the frequency range | f | ≤ W. Hence, the signal spectrum at the output of the ideal low pass filter is
- We require that the message signal at the output of the lowpass filter be undistorted.