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N. I. Achieser

Bio: N. I. Achieser is an academic researcher. The author has contributed to research in topics: Minimax approximation algorithm & Discrete dipole approximation codes. The author has an hindex of 2, co-authored 2 publications receiving 930 citations.

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Journal ArticleDOI
TL;DR: In this article, it was shown that a band-limited function f(t) is uniquely determined in terms of the samples g_k(nT) of the responses of m linear systems with input f (t), sampled at 1/m the Nyquist rate.
Abstract: It is shown that a band-limited function f(t) is uniquely determined in terms of the samples g_k(nT) of the responses g_k(t) of m linear systems with input f(t) , sampled at 1/m the Nyquist rate. Various known extensions of the sampling theorem follow as special cases of the resulting generalized sampling expansion of f(t) .

653 citations

Book ChapterDOI
J. Kiefer1
TL;DR: In this article, the authors discuss certain basic considerations such as the nonoptimality of the classical symmetric (balanced) designs for hypothesis testing, the optimality of designs invariant under an appropriate group of transformations, etc.
Abstract: After some introductory remarks, we discuss certain basic considerations such as the nonoptimality of the classical symmetric (balanced) designs for hypothesis testing, the optimality of designs invariant under an appropriate group of transformations, etc. In section 3 we discuss complete classes of designs, while in section 4 we consider methods for verifying that designs satisfy certain specific optimality criteria, or for computing designs which satisfy such criteria. Some of the results are new, while part of the paper reviews pertinent results of the author and others.

565 citations

Journal ArticleDOI
TL;DR: A new method of farthest point strategy for progressive image acquisition-an acquisition process that enables an approximation of the whole image at each sampling stage-is presented, retaining its uniformity with the increased density, providing efficient means for sparse image sampling and display.
Abstract: A new method of farthest point strategy (FPS) for progressive image acquisition-an acquisition process that enables an approximation of the whole image at each sampling stage-is presented. Its main advantage is in retaining its uniformity with the increased density, providing efficient means for sparse image sampling and display. In contrast to previously presented stochastic approaches, the FPS guarantees the uniformity in a deterministic min-max sense. Within this uniformity criterion, the sampling points are irregularly spaced, exhibiting anti-aliasing properties comparable to those characteristic of the best available method (Poisson disk). A straightforward modification of the FPS yields an image-dependent adaptive sampling scheme. An efficient O(N log N) algorithm for both versions is introduced, and several applications of the FPS are discussed.

407 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that the required number of elements is closely related to the desired sidelobe level and is almost independent of the aperture dimension, and the resolution or the beamwidth depends mainly on the aperture dimensions.
Abstract: Various probabilistic properties of a large antenna array with randomly spaced elements have been studied. It is found that for almost all cases of practical interest the required number of elements is closely related to the desired sidelobe level and is almost independent of the aperture dimension, the resolution (or the beamwidth) depends mainly on the aperture dimension, and the directive gain is proportional to the number of elements used if the average spacing is large. As a consequence the number of elements required is considerably less than that with uniform spacings. Starting with a given number of elements and a given aperture size, it is possible to improve the resolution by a factor of ten, a hundred, or more by spreading these elements over a larger aperture with little risk in obtaining a much higher sidelobe level and a lower directive gain. In fact, this method offers a solution which is optimum in a certain statistical sense, i.e., all sidelobes are of equal level with equal probability. In addition, this analysis also gives a simple estimate of the sidelobe level of most nonuniformly spaced antenna arrays. In a number of such arrays studied by various investigators with high speed computers, the agreement found is remarkable.

330 citations