ABSTRACT
In signal processing, it is of utmost importance to be able to find the exact number K of the constituent transients/harmonics of the investigated time signal. These transients lead to peaks/resonances in the corresponding frequency spectrum that need to be quantified. The first step in any reliable spectral quantification is an accurate determination of the number of transients. This chapter shows that the number of transients can be determined exactly through the Shanks transform for both non-degenerate (Lorentzian) and degenerate (non-Lorentzian) spectra. It demonstrates that the Shanks second-order transform represents the exact solution for a geometric sequence with two decaying transients. The chapter also applies the Shanks third-order transform to a geometric sequence with three decaying transients.
