Abstract
This article proposes a cost minimization approach to the problem of optimizing weighting digital windows used in classical 2-D spectral analysis. We suggest a general criterion form characterizing the 2-D spectral spreading caused by a window. Then this criterion is minimized and this results in an optimal shape of the window, extending an approach given by A. Papoulis in the case of monodimensional analog signals. We focus mainly on the minimization of a modification of the second order moment adapted to sampled signals. This leads to a natural extension of the optimal window of Papoulis to the case of 2-D digital signals. In the case of rectangular sampling, this optimal window is separable and has a simple analytical form. It is the product of two 1-D half period long cosine lobe windows. Results are also given in the case of hexagonal sampling. Other possible forms of the cost function are also discussed.
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le Roux, J. Weighting window optimization for classical 2-D spectral analysis. Multidim Syst Sign Process 2, 9–21 (1991). https://doi.org/10.1007/BF01940469
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DOI: https://doi.org/10.1007/BF01940469