Fourier-Based Spectral Analysis with Adaptive Resolution

Details Fourier-Based Spectral Analysis with Adaptive Resolution Fourier-Based Spectral Analysis with Adaptive Resolution

2008-02-11

arxiv.org/abs/0802.1348v2

Physics

Data Analysis, Statistics and Probability

31 pages including 10 figures. Fixed problem with computational complexity, so section 10 is rewritten and 3 more figures are

Scientific paper

Despite being the most popular methods of data analysis, Fourier-based techniques suffer from the problem of static resolution that is currently believed to be a fundamental limitation of the Fourier Transform. Although alternative solutions overcome this limitation, none provide the simplicity, versatility, and convenience of the Fourier analysis. The lack of convenience often prevents these alternatives from replacing classical spectral methods - even in applications that suffer from the limitation of static resolution. This work demonstrates that, contrary to the generally accepted belief, the Fourier Transform can be generalized to the case of adaptive resolution. The generalized transform provides backward compatibility with classical spectral techniques and introduces minimal computational overhead.

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