A generalized window approach to spectral estimation

An approach to spectral estimation is developed. The estimator is constructed from only two starting requirements: closeness to an original autocorrelation estimate and planarity, i.e., smoothness, of the corresponding spectral estimator. The inverse of the variance of the original autocorrelation estimate enters as a weight. By making various a priori assumptions about the variance, and by selecting two mathematical formulations of the planarity requirement, both the classical window and the maximum entropy methods result as special cases. Thus, the two methods are put together since they follow from the same starting requirements. Attention is given to the case where both the variance is estimated in terms of the original autocorrelation estimate, and planarity is forced by the minimization of a functional involving the absolute value of the power spectrum derivatives. A window method results but with a variance dependent window involving two parameters, the order of the derivative and a parameter equivalent to the window width. An application to a meteorological process is included as an illustration.