We discretize the Weyl product acting on symbols of modulation spaces, using a Gabor frame defined by a Gaussian function. With one factor fixed. the Weyl product is equivalent to a matrix multiplication on the Gabor coefficient level. If the fixed factor belongs to the weighted Sjostrand space M omega(infinity,1), then the matrix has polynomial or exponential off-diagonal decay, depending oil the weight omega. Moreover, if its operator is invertible on L(2), the inverse matrix has similar decay properties. The results are applied to the equation for the linear minimum mean square error filter for estimation of a nonstationary second-order stochastic process from a noisy observation. The resulting formula for the Gabor coefficients of the Weyl symbol for the optimal filter may be interpreted as a time-frequency version of the filter for wide-sense stationary processes, known as the noncausal Wiener filter.