The reconstruction of a band-limited function and its Fourier transform from a finite number of samples at arbitrary locations by singular value decomposition

摘要

A method for the stable interpolation of a bandlimited function known at sample instants with arbitrary locations in the presence of noise is given. Singular value decomposition is used to provide a series expansion that, in contrast to the method of sampling functions, permits simple identification of vectors in the minimum-norm space poorly represented in the sample values. Three methods, Miller regularization, least squares estimation, and maximum a posteriori estimation, are given for obtaining regularized reconstructions when noise is present. The singular value decomposition (SVD) method is used to interrelate these methods. Examples illustrating the technique are given.