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Quantum-Classical Algorithm for an Instantaneous Spectral Analysis of Signals: A Complement to Fourier Theory

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Document pages: 26 pages

Abstract: A quantum time-dependentspectrum analysis, or simply, quantumspectral analysis (QSA) is presented in this work, and it’s based on Schrödinger’sequation. In the classical world, it is named frequency in time (FIT), which is used hereas a complement of the traditional frequency-dependent spectral analysis based onFourier 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 lets 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 followingadvantages, among others: 1) compact support withexcellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminatephase 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.

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