Weighting window optimization for classical 2-\(D\) spectral analysis (Q1175237)

The author proposes a cost minimization approach to the problem of optimal 2-\(D\) window design. Earlier techniques for multidimensional spectral estimation and FIR filter design use finite extended weighting windows. A criterion for quantifying the spectral spreading caused by a window was proposed by Papoulis. This work is an extension to the work of Papoulis in the case of analog signals to digital signals. For a general formulation of a cost characterizing the frequency spreading due to a given weighting window, it is shown that the optimal window minimizing this cost has a characterization: It is the eigenvector associated with the minimal eigenvalue of a block Toeplitz matrix whose blocks are also Toeplitz. Results are given in the case of rectangular and hexagonal sampling.