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arXiv:quant-ph/9906010

Quantum Tomography Approach in Signal Analysis

Margarita A. Man’ko

Published Jun 2, 1999• 3 citations
arXivHTMLPDF

Abstract

Some properties of the fractional Fourier transform, which is used in information processing, are presented in connection with the tomography transform of optical signals. Relation of the Green function of the quantum harmonic oscillator to the fractional Fourier transform is elucidated.
DOI
10.48550/arxiv.quant-ph/9906010

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The concept of the fractional Fourier transform is framed within the context of quantum evolution operators. This point of view yields an extension of the above concept and greatly simplifies the underlying operational algebra. It is also proved that a multidimensional extension can be performed by using a biorthogonal multiindex harmonic oscillator basis. It is finally shown that most of the proposed physical interpretations of the fractional Fourier transform are just trivial consequences of the analysis developed in this paper.
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