Computer Science – Numerical Analysis
Scientific paper
2008-04-28
Computer Science
Numerical Analysis
11 pages, 8 figures, submitted to DSP Journal
Scientific paper
In the first part of the article it was discussed the possibility of function analysis using as a basis a couple of nonorthogonal functions and hence vectorial decomposition and a pure frequency dictionary. Here we switch to polar coordinates so needing only one nonorthogonal function as a basis. This decomposition appears to have an even greater range of application and many widespread consequences. It will be shown that, with the analysis method developed, any function, satisfying a rather loose requisite, can be a basis. The theory, with its two representations: vectorial and polar, appears to be the natural generalization of the Fourier Theorem to the case of nonorthogonal bases. The implications of the tool range from a reformulation of the eigenproblem to real world applications. Examples of analysis and reconstruction of functions using the given algorithms and generic bases will be given. Some applications that can promptly benefit from the tools developed here will be pointed out.
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