The Energy Spreading PONS Transform and its Applications

PONS, the Prometheus Orthonormal Set, is a suite of digital signal processing and data transmission algorithms whose genesis is found in a generalization of the Shapiro Polynomials. We begin with an overview of the mathematical and energy spreading features of PONS and then discuss a "Global Uncertainty Principle", which was the initial motivation for the PONS construction. Then we describe the elementary yet elegant construction by Harold Shapiro of his polynomials, and show the straightforward generalization of this construction which yields the PONS sequences and polynomials. After briefly comparing PONS with the Walsh Functions we outline possible mathematical interpretations of Energy Spreading. We conclude with a live demonstration showing the extreme robustness of PONS-transformed digital signals to noise and loss in a transmission channel.