2016/10/11 by Mario Mastriani, Mastriani, Mario
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · Engineering · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Fractal and DNA sequence analysis #Image and Signal Denoising Methods #Neural Networks and Applications #Optical Polarization and Ellipsometry #Spectroscopy and Chemometric Analyses
paper · pdf · doi:10.48550/arxiv.1611.02302
openalex publication_date 2016/10/11 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
A quantum time-dependent spectrum analysis, or simply, quantum spectral\nanalysis (QSA) is presented in this work, and it is based on Schrodinger\nequation, which is a partial differential equation that describes how the\nquantum state of a non-relativistic physical system changes with time. In\nclassic world is named frequency in time (FIT), which is presented here in\nopposition and as a complement of traditional spectral analysis\nfrequency-dependent based on Fourier theory. Besides, FIT is a metric, which\nassesses the impact of the flanks of a signal on its frequency spectrum, which\nis not taken into account by Fourier theory and even less in real time. Even\nmore, and unlike all derived tools from Fourier Theory (i.e., continuous,\ndiscrete, fast, short-time, fractional and quantum Fourier Transform, as well\nas, Gabor) FIT has the following advantages: a) compact support with excellent\nenergy output treatment, b) low computational cost, O(N) for signals and O(N2)\nfor images, c) it does not have phase uncertainties (indeterminate phase for\nmagnitude = 0) as Discrete and Fast Fourier Transform (DFT, FFT, respectively),\nd) among others. In fact, FIT constitutes one side of a triangle (which from\nnow on is closed) and it consists of the original signal in time, spectral\nanalysis based on Fourier Theory and FIT. Thus a toolbox is completed, which it\nis essential for all applications of Digital Signal Processing (DSP) and\nDigital Image Processing (DIP); and, even, in the latter, FIT allows edge\ndetection (which is called flank detection in case of signals), denoising,\ndespeckling, compression, and superresolution of still images. Such\napplications include signals intelligence and imagery intelligence. On the\nother hand, we will present other DIP tools, which are also derived from the\nSchrodinger equation.\n