Effects of intensity modulations on the power spectra of random processes
Abstract
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 wellknown locally stationary spectrum approximation. This expansion is especially useful when the fluctuation scales T_{σ} of the modulating functions are large in comparison with the fluctuation scales T_{z} of the modulated processes. The expansion can be interpreted as an asymptotic series in the parameter {T _{σ}}/{T _{z}}. For given scales T_{σ} and T_{z}, 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.
 Publication:

Journal of Sound Vibration
 Pub Date:
 December 1987
 DOI:
 10.1016/0022460X(87)904093
 Bibcode:
 1987JSV...119..451M