An Innovative Approach for Modeling the Digital Signal Processing

The essential purpose of this manuscript is to introduce for the current literature a new theoretical approach how to implement the process of encoding data using an unique treatment with respect to the digital signal processing. Some relationship between a set of digital pulses and a special class of the real polynomials, allow us to identify the generation of a single pulse with an intrinsic dependence with 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 it 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.