Computational accuracy and stability issues for the finite, discrete Gabor transform

A Gabor expansion may use highly nonorthogonal basis functions and consequently inherit accuracy and stability problems due to near singularity when computed digitally. Two methods to discretize the Gabor transform are studied from the viewpoint of controlling numerical properties: a Zak-transform-based method and a matrix method. Theoretical issues relating to the singular behavior of each are cited, and stabilization techniques are proposed. The validity of each technique is demonstrated by results of numerical experiments. It is concluded that stability and accuracy can usually be achieved in a digitally implemented Gabor transform by proper choice of algorithm and stabilization mechanism