Spectral properties and optimum reconstruction of randomly gated stationary random signals

The mathematical description of random samplers is generalized to cover randomly gated stationary random signals. It is shown that the spectral density of randomly gated signals is the sum of a complex convolution integral and its paraconjugate. When a random gating signal is generated by a parent gating signal, relationships between the characteristic functions associated with a random gate and those associated with a parent gate are given. The application of Wiener-Hopf theory to the design of optimum filters for the reconstruction of randomly gated signals is presented.