Multidimensional discrete convolution: Difference between revisions

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===Applications===

Helix transformations to implement recursive filters via convolution are used in various areas of signal processing. Although frequency ___domain Fourier analysis is effective when systems are stationary, with constant coefficients and periodically-sampled data, it becomes more difficult in unstable systems. The helix transform enables three-dimensional post-stack migration processes that can process data for three-dimensional variations in velocity.<ref name=":2" /> In addition, it can be applied to assist with the problem of implicit three-dimensional wavefield extrapolation.<ref>{{Cite journal|title = Exploring three-dimensional implicit wavefield extrapolation with the helix transform|last = Fomel|first = Sergey|date = 1997|journal = SEP Report|last2 = Claerbout|first2 = Jon|pages = 43–60|url = https://pdfs.semanticscholar.org/5993/a76fdb37d3b1a3dfba795d6ed596c608cec9.pdf#page|archive-url =179 https://web.archive.org/web/20190104124207/https://pdfs.semanticscholar.org/5993/a76fdb37d3b1a3dfba795d6ed596c608cec9.pdf|url-status = dead|archive-date = 2019-01-04}}</ref> Other applications include helpful algorithms in seismic data regularization, prediction error filters, and noise attenuation in geophysical digital systems.<ref name=":1" />

==Gaussian Convolution==