Nonstationary predictive deconvolution
Gary F. Margrave, Michael P. Lamoureux
We present a general method for construction of a uniform partition of unity ( POU) that is exact over a finite segment of the real line and whose individual windows are constructed from asymmetric Gaussians. The spacing between windows need have no relationship to the Gaussian half-width. We illustrate the uses of such POU's to decompose a signal into a discrete set of temporally localized signals which we call Gabor slices. We then apply this theory to construct a time-domain nonstationary deconvolution method based on gapped prediction filtering. We call this new method slicedecon because it operates directly on the individual Gabor slices. We also prescribe the construction of nonstationary autocorrelation functions as an analysis tool. We then compare slicedecon with the more established Gabor deconvolution or gabordecon. When the prediction filtering is unit-lag, we show that slicedecon achieves results comparable to gabordecon on a nonstationary (Q attenuation) synthetic. For lags greater than unity slicedecon appears to suppress, though not eliminate, periodicities in the nonstationary autocorrelation of a signal. Testing on a synthetic with multiples has not yet indicated any dramatic elimination of the unwanted multiple reflections.