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arXiv · 1502.03401

Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets

L. R. Soares·H. M. de Oliveira·R. J. Cintra·R. M. Campello de Souza
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Abstract

Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint time-frequency analysis is introduced. It is shown that any Fourier eigenfunction achieve isoresolution. It is shown that an isoresolution wavelet can be derived from each known wavelet family by a suitable scaling.

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L. R. Soares, H. M. de Oliveira, R. J. Cintra, R. M. Campello de Souza. 2015-02-11. Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets. https://arxiv.org/abs/1502.03401

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