Linear Properties of Trigonometric Polinomials with Applications

Abstract

This work summarizes the author’s algorithmic and mathematical research. It summarizes discoveries related to the mapping of restricted trigonometric polynomials, which have been called Asynchronous Sinusoidal Functions (ASF), mapped onto certain reals matrices, called Asynchronous Sinusoidal Matrices (ASM). From the analysis of these mappings, a series of properties and applications will emerge, which will be presented and exemplified throughout. Given the necessarily summarized nature of this work, its content has been balanced so that the aforementioned mathematical foundations are clear and sufficient, while leaving room for examples and applications. The applications will provide the possibility - unprecedented, in the author’s point of view - of identifying the component frequencies of a signal based on trigonometric polynomials using algebraic methods, which are distinct and novel with respect to Fourier Series, and with greater flexibility with respect to weighted and/or intervaldefined (picewise) signals.