Matrix reformulation of the Gabor transform

Rogelio Balart

doi:10.1117/12.57517

1 June 1992 Matrix reformulation of the Gabor transform

Rogelio Balart

Author Affiliations +

Optical Engineering, Vol. 31, Issue 6, (June 1992). https://doi.org/10.1117/12.57517

Abstract

We have observed that if one restricts the von Neumann lattice to N points on the time axis and M points in the frequency axis there are, by definition, only MN independent Gabor coefficients. If the data is sampled such thatthere are exactly MN samples, then the forward and inverse Gabor transforms should be representable as linear transformations in C_MN, the MN-dimensional vector space over the complex numbers, and the relationships that hold become matrix equations. These matrix equations are formulated, and some conclusions are drawn about the relative merits of using some methods as opposed to others, i.e., speed versus accuracy as well as whether or not the coefficients that are obtained via some methods are true Gabor coefficients.

Citation Download Citation

Rogelio Balart "Matrix reformulation of the Gabor transform," Optical Engineering 31(6), (1 June 1992). https://doi.org/10.1117/12.57517

Published: 1 June 1992

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