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Zbl 1054.94002
Borgnat, Pierre; Flandrin, Patrick
On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation.
(English)
[J] Appl. Comput. Harmon. Anal. 15, No. 2, 134-146 (2003). ISSN 1063-5203

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.
[Ilya S. Molchanov (Bern)]
MSC 2000:
*94A12 Signal theory
28A80 Fractals
94A14 Modulation and demodulation
26A27 Nondifferentiability of functions of one real variable

Keywords: Weierstrass function; time-frequency; chirps

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