Analysis and design of minimax-optimal interpolators

Studies the problem of interpolating a bandlimited signal from its nonuniform samples. The authors consider a class of interpolation algorithms that includes the least-squares optimal interpolator proposed by J.L. Yen, and derive a closed-form expression of the interpolation error for interpolators of this type. The expression for the interpolation error shows that the error depends on the eigenvalue distribution of a matrix, which is specified by the set of sampling points. The authors notice that the usual sinc-kernel interpolator is an approximation to the Yen interpolator, and suggest a method of choosing the weighting coefficients in the sinc-kernel interpolator. The new sinc-kernel interpolator is superior to the sinc interpolator with the usual Jacobian (area) weighting and is far easier to implement than the Yen interpolator.

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