Multiset Signal Processing and Electronics

TL;DR

This paper explores how multiset operations can be implemented in analog and digital electronics to enhance signal processing, pattern recognition, and deep learning applications, emphasizing simplicity and high performance.

Contribution

It introduces methods for implementing multiset operations in electronic circuits, enabling advanced signal processing capabilities with potential for broad applications.

Findings

Multiset operations can be effectively translated into electronic systems.

Proposed circuits achieve high-performance self and cross-correlation.

Potential applications include pattern recognition and deep learning.

Abstract

Multisets are an intuitive extension of the traditional concept of sets that allow repetition of elements, with the number of times each element appears being understood as the respective multiplicity. Recent generalizations of multisets to real-valued functions, accounting for possibly negative values, have paved the way to a number of interesting implications and applications, including respective implementations as electronic systems. The basic multiset operations include the set complementation (sign change), intersection (minimum between two values), union (maximum between two values), difference and sum (identical to the algebraic counterparts). When applied to functions or signals, the sign and conjoint sign functions are also required. Given that signals are functions, it becomes possible to effectively translate the multiset and multifunction operations to analog electronics, which is the objective of the present work. It is proposed that effective multiset operations capable of high performance self and cross-correlation can be obtained with relative simplicity in either discrete or integrated circuits. The problem of switching noise is also briefly discussed. The present results have great potential for applications and related developments in analog and digital electronics, as well as for pattern recognition, signal processing, and deep learning.