On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation. (Q1413114)

The authors provide a time-frequency interpretation of Weierstrass-Mandelbrot functions which puts emphasis on their possible decomposition on chirps, i.e. amplitude and frequency modulated signals of the form \(a(t)\exp\{i\psi(t)\}\) with \(\psi(t)=2\pi f\log t\), as an alternative to their standard Fourier-based representation. The authors consider examples of so-defined deterministic functions and their randomised variants and the relevant estimation problems.