ABSTRACT
This chapter deals with the main advantages of the Padé-based spectral analysis. Signal processing can be advantageously examined also from two other powerful theoretical strategies, i.e. the concept of transients and the method of moments. Transients are presently reviewed using the Shanks transform which stems from sequence-to-sequence mappings performed either in the time or in the frequency domain. One can apply the Shanks transform also to sequences comprised of the elements that are partial sums from the Maclaurin series of the total Green function. Further refinements of the results are expected when the iterated Shanks transforms are employed. These iterations are obtained by treating the results from the first Shanks sequence as a new entry to the Shanks transform. In this way, the second Shanks sequence is generated which could also be subjected to the Shanks transform and so forth. The iterated Shanks transforms exhibit enhanced convergence rates.
