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Article Dans Une Revue Signal Processing Année : 2022

Scale-Shift and Harmonic analysis approach to the Mellin transform for Discrete-time signals

Résumé

We investigate the scale-shift operator for discrete-time signals via the action of the hyperbolic Blaschke group. Practical implementation issues are discussed and given for any arbitrary scale, in the framework of very classical discrete-time linear filtering. Our group theoretical standpoint leads to a purely harmonic analysis definition of the Mellin transform for discrete-time signals. Explicit analytical expressions of the atoms of the discrete-time Fourier-Mellin decomposition are provided along with a simple algorithm for their computation. The so-defined scale-shift operator also allows us to establish a mathematical equivalence in between the discrete-time wavelet coefficients of a given discrete-time signal and the corresponding Voice-transform generated by a well-chosen unitary representation of the Hyperbolic Blaschke group, in the classical Hardy space of the unit disc.
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Dates et versions

hal-03835066 , version 1 (31-10-2022)

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Mor Ngom, Daniel Alpay, Mamadou Mboup. Scale-Shift and Harmonic analysis approach to the Mellin transform for Discrete-time signals. Signal Processing, 2022, 204, pp.108830. ⟨10.1016/j.sigpro.2022.108830⟩. ⟨hal-03835066⟩
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