On the Chirp Decomposition of Weierstrass-Mandelbrot Functions, and their Time-Frequency Interpretation

Pierre Borgnat (1) , Patrick Flandrin (1)

1 Phys-ENS - Laboratoire de Physique de l'ENS Lyon

Weierstrass–Mandelbrot functions are given a time–frequency interpretation which puts emphasis on their possible decomposition on chirps as an alternative to their standard, Fourier-based, representation. Examples of deterministic functions are considered, as well as randomized versions for which the analysis is applied to empirical estimates of statistical quantities.

Keywords: Weierstrass function; Time–frequency; Mellin Transform; Chirps

Domains: Computer Science [cs]; Signal and Image Processing; Engineering Sciences [physics]; Signal and Image processing

Pierre Borgnat, Patrick Flandrin. On the Chirp Decomposition of Weierstrass-Mandelbrot Functions, and their Time-Frequency Interpretation. Applied and Computational Harmonic Analysis, 2003, 15, pp.134-146. ⟨ensl-00175961⟩