Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets

2015/02/11 by L. R. Soares, Soares, L. R., H. M. de Oliveira +6
Computer Science · Engineering · Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Image and Signal Denoising Methods #Machine Fault Diagnosis Techniques #Ultrasonics and Acoustic Wave Propagation #math.CA

paper · pdf · doi:10.48550/arxiv.1502.03401

6 pages, XX Simpósio Bras. de Telecomunicações, Rio de Janeiro, Brazil, 2003. Fixed typos

openalex publication_date 2015/02/11 · arxiv created 2015/02/17 · arxiv updated 2015/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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