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

Mor Ngom, Daniel Alpay, Mamadou Mboup

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Article number108830
JournalSignal Processing
StatePublished - 1 Mar 2023
Externally publishedYes


  • Discrete Wavelet Transform
  • Discrete-time Scale-Shift
  • Hyperbolic Blaschke group
  • Mellin transform
  • Voice-Transform

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Software
  • Signal Processing
  • Computer Vision and Pattern Recognition
  • Electrical and Electronic Engineering


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