Fourier Eigenfunctions, Uncertainty Gabor Principle and Isoresolution Wavelets
L. R. Soares, H. M. de Oliveira, Renato J. Cintra, de Souza, R. M. Campello · arXiv (Cornell University) · 2015
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.