Noise reduction in tight Weyl-Heisenberg frames

The functions g that give rise to tight Weyl-Heisenberg frames based on time and frequency discretization steps q/sub 0/ and p/sub 0/, with p/sub 0/q/sub 0/=(2 pi )/k(k in N), are characterized, and the noise reducing properties of such frames are examined. It is shown that when the frame coefficients c/sub m,n/(f) of a function f are subject to stationary noise n, the average squared L/sup 2/-norm of the corresponding noise-contribution to the reconstruction of f is down by a factor proportional to k/sup 2/ for a fixed number of sample points. Also, a measure of local error of the reconstruction is introduced as opposed to the global L/sup 2/-error. For a given noise n, formulae are derived for the optimal choice (or choices) of the basis function g, in the sense of minimizing this local error.<>