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.
Details
The random modulation procedure starts with two stochastic
baseband signals, and , whose
frequency spectrum is non-zero only for . It applies
quadrature modulation to combine these with a carrier frequency (with ) to form the signal given by
In the following it is assumed that and are two real jointly
wide sense stationary processes. It can be shown[citation needed] 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
Papoulis, Athanasios; Pillai, S. Unnikrishna (2002). "Random walks and other applications". Probability, random variables and stochastic processes (4th ed.). McGraw-Hill Higher Education. pp. 463–473.
Scarano, Gaetano (2009). Segnali, Processi Aleatori, Stima (in Italian). Centro Stampa d'Ateneo.
Papoulis, A. (1983). "Random modulation: A review". IEEE Transactions on Acoustics, Speech, and Signal Processing. 31: 96–105.
doi:
10.1109/TASSP.1983.1164046.