ABSTRACT
This chapter ties the Shanks transform to the spectral harmonic analysis for the discrete auto-correlation function and time signal. It considers a model sequence viewed as the input data to the so-called reconstruction/retrieval/decomposition problem or the generalized harmonic inversion problem. The chapter illustrates how the Shanks transform finds exactly all the unknown parameters of the sequence to complete the task of spectral analysis. Practitioners dealing with statistical data often encounter so-called outliers, i.e. data that single themselves out by being very different from the rest. Such data are often discarded or artificially manipulated when simple averaging is used. The Euler sequential averaging is expected to mitigate this problem with outliers in a more satisfactory and systematic way. In signal processing, the outliers are conceived as possible rare spectral features that cannot be reconstructed by using only the principal components.
