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On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation. (English) Zbl 1054.94002
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.

94A12Signal theory (characterization, reconstruction, filtering, etc.)
94A14Modulation and demodulation
26A27Nondifferentiability of functions of one real variable; discontinuous derivatives
Full Text: DOI
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