Quadrature modulation

Quadrature modulation is the general technique of combining two amplitude-modulated (DSB) carrier signals in such a way that the original amplitude modulations are separable, by coherent demodulation, at the receiver. Examples include quadrature amplitude modulation, phase-shift keying, and minimum-shift keying. Constellation diagrams are used to examine the modulation in the 2-D signal space.

With typical constraints on the two amplitude modulation waveforms, quadrature modulation can result in a single constant-envelope, phase-modulated carrier described mathematically by the trigonometric identity:

and equivalently:

where:

Both carrier frequencies are ${\displaystyle f_{c}}$ Hz, and the first one lags the second one by π/2 radians (90 degrees). It is in-phase with the composite waveform, and its amplitude modulation is designated by I(t). The other carrier is said to be in-quadrature with the first, and its amplitude modulation is designated by Q(t). The 90° phase difference between the original carriers makes them orthogonal, which is key to the subsequent separability of the modulations. Another key is that the modulations are low-frequency/low-bandwidth waveforms compared to ${\displaystyle f_{c},}$  which is known as the narrowband assumption.

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