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In the theories of modulation and of stochastic processes, random modulation is the creation of a new signal from two other signals by the process of quadrature amplitude modulation. In particular, the two signals are considered as being random processes. For applications, the two original signals need have a limited frequency range, and these are used to modulate a third sinusoidal carrier signal whose frequency is above the range of frequencies contained in the original signals.
In the following it is assumed that and are two real jointly wide sense stationary processes. It can be shown that the new signal is wide sense stationary if and only if is circular complex, i.e. if and only if and are such that