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Optimal filter for unknown signal


Yu.G. Tratas

The problem of determining the weight function of the optimal linear filter that provides maximum signal / noise ratio for receiving the pulse signal, the shape of which is not known a priori id considered. It is proposed to use for this purpose the results of repeated observation segments input receiver. This task is relevant for systems using chaotic oscillations due to their inherent properties of the \"exponential divergence of trajectories.\" It is shown that the solution of the integral equation for the optimal weight function does not change, if the task receiving the pulse signal is replaced by the sum of the task receiving the signal and additive noise. Bred recursive algorithm for solving an integral equation using as the correlation function for the sum of the signal and noise evaluation, obtained from the input receiver is designed. We propose a way to ensure sustainable convergence priori recursive algorithm to the correct solution. An example of a mathematical modeling procedure for determining the weighting function for the pulse of the chaotic signal, described by the mapping, called the Bernoulli shift, and takes in white Gaussian noise. It is concluded that the results obtained in this work are applicable to arbitrary pulse signals.
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