Abstract
The essential purpose of this paper is to introduce to the current literature a new theoretical approach on how to implement the process of encoding data using a unique treatment with respect to the digital signal processing. Some relationships between a set of digital pulses and a special class of real polynomials allow us to identify the generation of a single pulse with an intrinsic dependence on the zero values of an arbitrary equation represented by a polynomial equation, where this direct match is established through an analytic operator. By using an ordinary field-programmable gate array architecture, it is possible to validate our theoretical approach, and we are presenting some experimental measurements, as well as one application on how to build a commercial data compressor for fiber optics. The algorithm here introduced presents an innovative technique, and its performance is faster per comparison. Furthermore, thanks to the math-to-time-domain transformations, it tends to overcome the current time required to process polynomial equations, which are involved in the data compression and data encryption systems.
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