6 April 1995 Structural properties of Gabor transforms and numerical algorithms
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Abstract
Let g be a Gabor window of length N, (a,b) be a pair of lattice constants. The time and frequency translates {MmbTnag} of g forms so-called Gabor family (or Weyl-Heisenberg wavelet system). In this note, we present the structural properties of the discrete Gabor transforms, and determine the best approximation of a signal (chi) (epsilon) $CBARN in a very general case by linear combinations from a given Gabor family (we do not assume here whether this family forms a frame or not). For this task, we are determining the (generalized) dual Gabor atom. We propose the conjugate-gradient (CG)- method with O(N) complexity for fixed lattice constants (a,b) to solve the problem.
© (1995) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Sigang Qiu, Sigang Qiu, } "Structural properties of Gabor transforms and numerical algorithms", Proc. SPIE 2491, Wavelet Applications II, (6 April 1995); doi: 10.1117/12.205457; https://doi.org/10.1117/12.205457
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