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NAFASS: Discrete spectroscopy of random signals |
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| Authors: | RR Nigmatullin SI Osokin VA Toboev |
| Institution: | 1. Institute of Physics, Kazan (Volga Region) Federal University, Kremlevskaya str.18, Kazan, Tatarstan 420008, Russia;2. Department of Mathematics, Chuvash State University, Moskovskiy pr.,15, Cheboksary 428015, Russia;1. Department of Mathematics, Zhangzhou Normal University, Zhangzhou, 363000, PR China;2. Department of Mathematics, South China University of Technology, Guangzhou, 510641, PR China;1. Departamento de Matematicas, Centro Universitario de Ciencias Exactas e Ingenierias, Universidad de Guadalajara, Mexico;2. Heilbronn Institute for Mathematical Research, School of Mathematics, University of Bristol, University Walk, Bristol, BS8 1TW, UK;1. Department of Computer Science, University of Puerto Rico - Río Piedras;2. Department of Mathematics, University of Puerto Rico - Río Piedras;1. Department of Mathematics, Shandong University, Jinan, Shandong 250100, PR China;2. Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330031, PR China;1. USDA-Agricultural Research Service, Wind Erosion & Water Conservation Research Unit, Lubbock, TX, USA;2. The University of Texas at El Paso, Department of Chemistry, El Paso, TX 79968, USA;3. USDA-ARS, Central Great Plains Research Station, 40335 County Road GG, Akron, CO 80720, USA;4. USDA-Agricultural Research Service, Wind Erosion & Water Conservation Research Unit, Big Spring, TX, USA;5. Department of Soil Science, North Carolina State University, Raleigh, NC 27695-7619, USA;6. Atmospheric Environment Research Centre, Griffith School of Environment, Griffith University, Brisbane, Australia |
| Abstract: | In this paper we suggest a new discrete spectroscopy for analysis of random signals and fluctuations. This discrete spectroscopy is based on successful solution of the modified Prony’s problem for the strongly-correlated random sequences. As opposed to the general Prony’s problem where the set of frequencies is supposed to be unknown in the new approach suggested the distribution of the unknown frequencies can be found for the strongly-correlated random sequences. Preliminary information about the frequency distribution facilitates the calculations and attaches an additional stability in the presence of a noise. This spectroscopy uses only the informative-significant frequency band that helps to fit the given signal with high accuracy. It means that any random signal measured in t-domain can be “read” in terms of its amplitude-frequency response (AFR) without model assumptions related to the behavior of this signal in the frequency region. The method overcomes some essential drawbacks of the conventional Prony’s method and can be determined as the non-orthogonal amplitude frequency analysis of the smoothed sequences (NAFASS). In this paper we outline the basic principles of the NAFASS procedure and show its high potential possibilities based on analysis of some actual NIR data. The AFR obtained serves as a specific fingerprint and contains all necessary information which is sufficient for calibration and classification of the informative-significant band frequencies that the complex or nanoscopic system studied might have. |
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