A multidimensional approach to evolutionary spectrum estimation

Smoothing of the Wigner distribution introduces two-dimensional sequences which bring the theory of two-dimensional filter analysis and design to the one-dimensional time-varying spectrum estimation. In this study, the region of support of the two-dimensional filters associated with the commonly used periodogram, averaged periodograms, and Wigner estimators are defined and used to express, through the singular value decomposition, the periodograms-based estimators as a linear combination of the pseudo-Wigner estimators (PWE). The PWE associated with the maximum singular value of the eigenvector expansion of the periodogram is viewed as the closest approximation between the two estimators. Error bounds are derived, and simulations are performed to demonstrate the effects of limiting the expansion to the dominant singular values, i.e. using a reduced rank periodogram