Quantum-classical algorithm for an instantaneous spectral analysis of signals: a complement to Fourier Theory - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year :

Quantum-classical algorithm for an instantaneous spectral analysis of signals: a complement to Fourier Theory

Mario Mastriani
  • Function : Author
  • PersonId : 1024326

Abstract

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it's based on Schrödinger's equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum-not taken into account by Fourier theory and let alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: a) compact support with excellent energy output treatment, b) low computational cost, O(N) for signals and O(N 2) for images, c) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.
Fichier principal
Vignette du fichier
manuscript.pdf (968.15 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01735776 , version 1 (16-03-2018)
hal-01735776 , version 2 (26-12-2018)

Identifiers

  • HAL Id : hal-01735776 , version 2

Cite

Mario Mastriani. Quantum-classical algorithm for an instantaneous spectral analysis of signals: a complement to Fourier Theory. 2018. ⟨hal-01735776v2⟩
52 View
255 Download

Share

Gmail Facebook Twitter LinkedIn More