Efficient Analysis and Synthesis using a New
Factorization of the Gabor Frame Matrix.
S. Moreno, F.J. Ferri, M. Arevalillo, W. Diaz
http://www.uv.es/prcv
Abstract
In this paper, we consider the
case in which one needs to carry out Gabor analysis and synthesis on
large signals using a short support analysis window and its
corresponding, possibly longer canonical dual window, respectively. In
this asymmetric context, we propose a novel factorization of the Gabor
frame operator that exploits its strong and well-known structure and
leads to a computational cost for synthesis which is only slightly
above the one needed for short support analysis.
The proposed factorization applies to any Gabor system with very mild
conditions and leads to a potentially promising alternative to current
synthesis algorithms in the case of short analysis windows slightly
above the number of frequency channels
Graphical abstract
Cost illustration
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