3 research outputs found
On causal extrapolation of sequences with applications to forecasting
The paper suggests a method of extrapolation of notion of one-sided
semi-infinite sequences representing traces of two-sided band-limited
sequences; this features ensure uniqueness of this extrapolation and
possibility to use this for forecasting. This lead to a forecasting method for
more general sequences without this feature based on minimization of the mean
square error between the observed path and a predicable sequence. These
procedure involves calculation of this predictable path; the procedure can be
interpreted as causal smoothing. The corresponding smoothed sequences allow
unique extrapolations to future times that can be interpreted as optimal
forecasts.Comment: arXiv admin note: substantial text overlap with arXiv:1111.670
Band-limited extrapolation on the sphere for signal reconstruction in the presence of noise
We investigate the problem of extrapolation of band-limited signals on the 2-sphere in the presence of noise. Specifically, given incomplete or spatially limited measurements subject to noise, find the unique extrapolation to the complete 2-sphere. We present an analytic solution to the extrapolation problem based on the expansion of a signal in Slepian basis corresponding to an orthogonal set of eigenfunctions of an associated energy concentration problem. An alternative equivalent iterative algorithm is also developed for practical implementation and guidelines are proposed to choose the parameters of the iterative algorithm. The capability of the proposed extrapolation is compared and demonstrated with the help of an illustration example