Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets

L. R. Soares, H. M. de Oliveira, R. J. de S. Cintra, R. M. C. de Souza

DOI: 10.14209/sbrt.2003.372

Evento: XX Simpósio Brasileiro de Telecomunicações (SBrT2003)

Keywords: Gabor-Heisenberg inequality Fourier eigenfunctions time-frequency analysis isoresolution wavelets.

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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