A Generalization of the Fourier Transform and its Application to Spectral Analysis of Chirp-like Signals

Abstract : We show that the de Branges theory provides a useful generalization of the Fourier Transform (FT). The formulation is quite rich in that by selecting the appropriate para\-me\-trization, one can obtain spectral representation for a number of important cases. We demonstrate two such cases in this paper: the finite sum of elementary chirp-like signals, and a decaying chirp using Bessel functions. We show that when defined in the framework of de Branges spaces, these cases admit a representation very much similar to the spectral representation of a finite sum of sinusoids for the usual FT.
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Applied and Computational Harmonic Analysis, Elsevier, 2011, 〈10.1016/j.acha.2011.11.002〉
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Mamadou Mboup, Tülay Adali. A Generalization of the Fourier Transform and its Application to Spectral Analysis of Chirp-like Signals. Applied and Computational Harmonic Analysis, Elsevier, 2011, 〈10.1016/j.acha.2011.11.002〉. 〈hal-00640508v2〉

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