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I have a time series that has been measured after convolution with a moving average filter. Knowing the parameters of the moving average filter, is it possible to reconstruct/constrain the values of the original? When considering deconvolution, there is much discussion in the literature of the form and magnitude of measurement error, but the variation in signal due to this component is much less than the non-stationary component (generated by the physical process generating the signal), if that knowledge helps in the analysis. This is not my primary domain of expertise so my apologies if it is a simple question (even getting a gauge of whether this is simple or difficult would be helpful). I wonder if I need to look into Gabor deconvolution or other topics that would help me understand an approach to this problem. Thanks very much.

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