SSB generation with Quadrature modulation

One method of performing single sideband modulation is to employ a quadrature modulator. A quadrature modulator mixes the message with two carriers. Both carriers operate at the same frequency, but are shifted in phase by 90 degrees relative to one another (hence the “quadrature” term). This simply means that the two carriers can be expressed as cos(2πfct) and sin(2πfct).

The message, too, is modified to consist of two separate signals: the original and a 90 degree phase-shifted version of the original. The original is mixed with the cosine component of the carrier and the phase-shifted version is mixed with the sine component of the carrier. These two modifications result in the implementation of the single sideband function.

Trigonometrically, this can be expressed as:

Just by changing the sign of the left hand side term i.e. to negative from positive we can easily get the upper sideband only.