Band-limited Functions: / / -convergence
نویسندگان
چکیده
منابع مشابه
A Reconstruction Method for Band-Limited Signals on the Hyperbolic Plane
A notion of band limited functions is considered in the case of the hyperbolic plane in its Poincare upper half-plane H realization. The concept of band-limitedness is based on the existence of the Helgason-Fourier transform on H. An iterative algorithm is presented, which allows to reconstruct bandlimited functions from some countable sets of their values. It is shown that for sufficiently den...
متن کاملSampling and Frequency Warping
Optimal sampling of non band-limited functions is an issue of great importance that has attracted considerable attention. We propose to tackle this problem through the use of a frequency warping: First, by a non-linear shrinking of frequencies, the function is transformed into a band-limited one. One may then perform a decomposition in Fourier series. This process gives rise to new orthonormal ...
متن کاملAPPROXIMATING NON - BAND - LIMITED FUNCTIONS BY NONUNIFORMSAMPLING SERIESPaulo
We describe a new method of approximating a class of non-band-limited functions by nite nonuniform sampling series. The method is based on a simple idea: that of approximating a convolution integral by a nite sum, and then using the nite sum to obtain an upper bound for the approximation error. The sampling series do not have to be based on the usual sin(wt)=(t) kernel, and their convergence ca...
متن کاملOn the Stability of Certain Interpolation Problems
In this work we present a number of results concerning the nite dimensional band-limited interpolation problem. Our aim is to understand how the stability of the interpolation problem is aaected by changes in the positions of the interpolation knots. We give upper and lower bounds for the eigenvalues of the interpolation matrix, as functions of the gaps between missing samples. The upper bound ...
متن کاملA Reconstruction Formula for Band Limited Functions in L2(r)
It is shown that a band limited function from L2(R) can be reconstructed from irregularly sampled values as a limit of spline functions. The assumption about the sampling sequence is that it should be dense enough. It is known that band limited functions, i.e. functions whose Fourier transform have compact support, are uniquely determined and can be recovered from their values on specific discr...
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