Optimal design of windows for spectral analysis of mono and bidimensional sampled signals

The problem of digital window design is formulated in terms of cost minimization. This cost quantifies the leakage from one frequency to another. The choice of the penalty function appearing in the cost expression may be adapted to a given spectral analysis problem: the designer controls undesirable leakages. The approach is applied to a particular optimization problem: extending the minimization of the second order moment to the case of sampled signals spectra. This example leads to a correct justification of Papoulis´ (1972) minimum energy moment window in the case of digital signals. Applications show an example of window design and the interest of Papoulis window in some problems of spectral parameters estimation: Pisarenko frequency estimation and autoregressive modelization. The extension to 2D signals is given