16 - Back to Examples

Summary

The different examples that had been used in Section 1 as motivations, are revisited at the light of what has been discussed later. The bat echolocation case is considered in a greater generality, with considerations about sequences of calls and the “why and how” of their structure in terms of optimality. Time-frequency formulations of matched filtering are proposed and used for, e.g., supporting in a geometrical way the solution to Doppler-tolerance. A similar analysis is provided for gravitational waves, with signal denoising complemented by parameter estimations and comparisons with theoretical models. Finally, Riemann’s zeta-function, as well as variations thereof and Weierstrass' functions, are given a time-frequency interpretation based on their disentanglement into chirp components.