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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{iψ(t)} with ψ(t)=2πflogt, 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.
MSC:
94A12Signal theory (characterization, reconstruction, filtering, etc.)
28A80Fractals
94A14Modulation and demodulation
26A27Nondifferentiability of functions of one real variable; discontinuous derivatives