The Reconstruction of a Band-Limited its Fourier Transform From a Finite Samples at Arbitrary Locations by Value Decomposition
Duncan J. Winghani · 1992
A method for the stable interpolation of a band- limited function known at sample instants with arbitrary lo- cations in the presence of noise is given. Sbrgular value decom- position is used to provide a series expansion that, in contrast to the method of sampling functions, permits simple identifi- cation of vectors in the minimum-norm space poorly repre- sented in the sample values. When noise is present, we give three methods, Miller regularization, least squares estimation, and maximum a posteriori estimation, for obtaining regularized reconstructions. The singular value decomposition method is used to interrelate these methods. Examples illustrating the technique are given.