TL;DR
This paper introduces a novel method for calculating harmonic transforms efficiently for signals of arbitrary dimensions, utilizing matrix multiplication and establishing connections between coordinate systems to improve conformal mapping and signal analysis.
Contribution
It presents a new approach to harmonic transform calculation, connecting rectangular and polar coordinates, and introduces a robust iterative algorithm for conformal mapping.
Findings
Efficient computation of harmonic transforms for arbitrary signal dimensions.
A new ratio and method for analyzing two oscillative signals.
Development of a robust iterative algorithm for conformal mapping.
Abstract
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital representation by reducing the transform to a vector-to-circulant matrix multiplying. There is a connection between harmonic equations in rectangular and polar coordinate systems. The connection established here and used to create a very robust iterative algorithm for a conformal mapping calculation. There is also suggested a new ratio (and an efficient way of computing it) of two oscillative signals.
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Taxonomy
TopicsSensor Technology and Measurement Systems