A cost minimization approach for optimal window design in spectral analysis of sampled signals

The problem of digital window design is formulated in terms of cost minimization. This cost quantizes the leakage from one frequency to another. The choice of the penalty function appearing in the cost expression may be adapted to a specific spectral analysis problem and allows the designer to control undesirable leakages. The approach is applied in one particular optimization problem: the minimization of the second-order moment extension to the case of sampled signal spectra. This example leads to a correct justification of the Papoulis (1977) window in the case of digital signals. Applications show examples of window design and the interest in the Papoulis window in some problems of spectral parameters estimation: Pisarenko (1973) frequency estimation and autoregressive modelization