A new signal processing tool developed with the help of the Clifford algebra

Abstract

A positive integer is expressed as a sum of squares of positive integers in a unique way applying a special technique. The expression, thus obtained is resolved into two factors using the concept of the Clifford algebra. This technique is applied on a set of positive integers. Using these factors, a new mean of the set of integers, different from the arithmetic mean, is developed. A detailed discussion involving Cl(0,3) as an example is presented. The new mean bears the imprint of degree of randomness of the data set. More random is the data set more away is the new mean from the arithmetic mean. It is suggested that this averaging technique may be useful in signal and image processing with some special gain. Keywords New mean, Clifford algebra.