# Single Sideband and Vestigial Sideband Modulation.

Cuthbert Nyack
Since the 2 sidebands in a DSB signal carry the same information, then one can go furthur in improving the efficiency of the transmission by transmitting only 1 sideband(upper or lower one can be used). The resulting signal is referred to as single sideband SSB.

The yellow curve below shows an SSB signal. It consists of a wave whose amplitude and frequency changes as the the amplitude and frequency of the modulating signal changes. Red curve in applet shows the AM signal which results when the SSB signal is added to a carrier(shown in blue) which is generated in the receiver. Changing the scrollbars show that the envelope of the AM is not much affected by the phase of the introduced carrier fcr.

Changing the frequency wcr of the carrier produced in the receiver causes the frequency of the modulation to change but the general shape remains the same(shown by cyan line). It is apparent that the envelope of the red curve does not coincide with the green curve. This is an example of SSB distortion, it can be affected by the relative magnitudes of am and ac but never goes away.

Fn = 1 and 2 shows the amplitude and phase distortion which is a consequence of using only one sideband Fn = 1 shows upper sideband and Fn = 2 shows lower sideband distortion.

Fn = 3 and 4 compares the phasor representation of AM and SSB signals. Pt moves the phasor horizontally. Fn = 3 shows the sideband doubled for comparison with AM.

Fn = 5 shows the spectrum of a VSB signal(reproduced below) as used in NTSC video. For some signals like video, there is no lower limit to the sideband frequency because the low frequencies are needed to represent slowly varying video information. Instead of trying to filter off a sideband, a portion of the lower sideband is transmitted as shown below. The complete upper sideband is from fc to f3 and the vestigial lower sideband is from f1 to fc.
To avoid overemphasising the lower frequencies, the receiver filters the received signal to look as shown by the bottom spectrum.
For frequencies between fc and f2 a portion of upper and lower sidebands is processed.
Fn = 6 shows the amplitude and phase distortion for VSB signals. For frequencies between f2 and f3 the distortion is the same as for SSB signals. Between fc and f2 the distortion is less starting at zero at fc and reaching SSB levels at f2. This can be seen by varying 'a' between 0.5 and 1.0.

Fn = 7 shows a comparison of the phasor representation of AM and VSB. Changing Pt moves the phasor horizontally and changing 'a' changes the relative magnitude of the sidebands.