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Analysis And Design Of MinimaxOptimal Interpolators
 IEEE Trans. Signal Proc
, 1998
"... We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix which is specified for each set of sa ..."
Abstract

Cited by 13 (3 self)
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We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix which is specified for each set of sampling points. The error expression can be used to prove that the Yen interpolator is optimal. The implementation of the Yen algorithm suffers from numerical illconditioning, forcing the use of a regularized, approximate solution. We suggest a new, approximate solution, consisting of a sinckernel interpolator with specially chosen weighting coefficients. The newly designed sinckernel interpolator is compared with the usual sinc interpolator using Jacobian (area) weighting, through numerical simulations. We show that the sinc interpolator with Jacobian weighting works well only when the sampling is nearly uniform. The newly designed sinckernel interpolator is shown to perform better than ...
Analysis and Design of
"... Abstract — We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix that is specified for each ..."
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Abstract — We consider a class of interpolation algorithms, including the leastsquares optimal Yen interpolator, and we derive a closedform expression for the interpolation error for interpolators of this type. The error depends on the eigenvalue distribution of a matrix that is specified for each set of sampling points. The error expression can be used to prove that the Yen interpolator is optimal. The implementation of the Yen algorithm suffers from numerical ill conditioning, forcing the use of a regularized, approximate solution. We suggest a new, approximate solution consisting of a sinckernel interpolator with specially chosen weighting coefficients. The newly designed sinckernel interpolator is compared with the usual sinc interpolator using Jacobian (area) weighting through numerical simulations. We show that the sinc interpolator with Jacobian weighting works well only when the sampling is nearly uniform. The newly designed sinckernel interpolator is shown to perform better than the sinc interpolator with Jacobian weighting. I.