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

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1 Author(s)
Wingham, D.J. ; Dept. of Electron. & Electr. Eng., Univ. Coll., London, UK

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

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Signal Processing, IEEE Transactions on  (Volume:40 ,  Issue: 3 )