In this paper we show how to construct a certain class of orthonormal bases in starting from one or more Gabor orthonormal bases in . Each such basis can be obtained acting on a single function with a set of unitary operators which operate as translation and modulation operators in suitable variables. The same procedure is also extended to frames and wavelets. Many examples are discussed.
BAGARELLO F (2008). Gabor-like systems in ${cal L}^2({bf R}^d)$ and extensions to wavelets. JOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL, 41, 335208-1-335208-15 [10.1088/1751-8113/41/33/335208].
Gabor-like systems in ${cal L}^2({bf R}^d)$ and extensions to wavelets
BAGARELLO, Fabio
2008-01-01
Abstract
In this paper we show how to construct a certain class of orthonormal bases in starting from one or more Gabor orthonormal bases in . Each such basis can be obtained acting on a single function with a set of unitary operators which operate as translation and modulation operators in suitable variables. The same procedure is also extended to frames and wavelets. Many examples are discussed.
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