Application of Stochastic Approximation to Frequency Domain Adaptive Filters.

摘要

The research described is concerned with developing a system for adaptively processing the outputs of an array of sensing elements subject to certain optimality and processing time constraints. The adaptive part of the processor is designed to be a stochastic adaptive filter so that the processor can handle the inputs which are random processes. The processor is also recursive so as to be easily updated as the environment changes. In the development of the theory of the stochastic adaptive filter, the orthogonal projection lemma is used to perform the minimization of the complex variable problem resulting from these frequency domain considerations. Using the results of the minimization, a special recursive algorithm used to obtain the matrix filter coefficients used in the adaptive processor is derived from the theory of stochastic approximation. The special recursive stochastic algorithm is shown to be a frequency domain multi-input, multi-output adaptive realization of the Wiener filter, and has as its goals, operating as an adaptive processor, the ability to gain fast increase in output signal-to-noise (S/N) and yet maintain statistical smoothing characteristics necessary for practical real time use of an adaptive processor. (Author)