Effects of intensity modulations on the power spectra of random processes

An intensity modulated random process {x(t)} is defined as the product of a deterministic modulating function σ(t) or modulating process {σ(t)} and a stationary modulated process {z(t)} that is statistically independent of {σ(t)}. General expressions for the instantaneous power spectra of intensity modulated processes are derived for various classes of modulating functions and processes. A series expansion of the instantaneous power spectrum of intensity modulated processes is derived which has for its first term a well-known locally stationary spectrum approximation. This expansion is especially useful when the fluctuation scales Tσ of the modulating functions are large in comparison with the fluctuation scales Tz of the modulated processes. The expansion can be interpreted as an asymptotic series in the parameter TσTz. For given scales Tσ and Tz, it is shown that modulating processes {σ(t)} possessing no first derivative have a substantially larger effect on the power spectrum of modulated processes {z(t)} than modulating processes possessing a first derivative. Four examples illustrating various aspects of the theory are provided.

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