Processing of large sets of stochastic signals: filtering based on piecewise interpolation technique

TL;DR

This paper introduces a novel filtering method for large stochastic signal sets using an extended piecewise interpolation technique, enabling effective filtering with limited prior information and ensuring filter existence via pseudo-inverse matrices.

Contribution

It presents a new filtering approach based on extended piecewise interpolation that requires minimal prior data and applies to large random signal sets.

Findings

Filter outperforms traditional methods with limited prior info

Single filter applicable to any signal in large sets

Filter existence guaranteed by pseudo-inverse matrices

Abstract

Suppose $K_{_Y}$ and $K_{_X}$ are large sets of observed and reference signals, respectively, each containing $N$ signals. Is it possible to construct a filter $F$ that requires a priori information only on few signals, $p\ll N$, from $K_{_X}$ but performs better than the known filters based on a priori information on every reference signal from $K_{_X}$? It is shown that the positive answer is achievable under quite unrestrictive assumptions. The device behind the proposed method is based on a special extension of the piecewise linear interpolation technique to the case of random signal sets. The proposed technique provides a single filter to process any signal from the arbitrarily large signal set. The filter is determined in terms of pseudo-inverse matrices so that it always exists.