Journal ArticleDOI
NAFASS: Discrete spectroscopy of random signals
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TLDR
The basic principles of the NAFASS procedure are outlined and its high potential possibilities based on analysis of some actual NIR data are shown.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.read more
Citations
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Journal ArticleDOI
A new collection of real world applications of fractional calculus in science and engineering
TL;DR: This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus that will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool.
Journal ArticleDOI
Coding Prony’s method in MATLAB and applying it to biomedical signal filtering
A. Fernández Rodríguez,L. de Santiago Rodrigo,E. López Guillén,J. M. Rodríguez Ascariz,J. M. Miguel Jiménez,Luciano Boquete +5 more
TL;DR: This paper provides a tutorial on the main polynomial Prony and matrix pencil methods and their implementation in MATLAB, provides the MATLAB code needed to implement the classic, LS, TLS and MPM methods, and tests their performance in biomedical signal filtering and function approximation.
Journal ArticleDOI
NIMRAD: novel technique for respiratory data treatment
TL;DR: This paper illustrates the efficiency and simplicity of a new technique which is determined in this paper as NIMRAD (the non-invasive methods of the reduced analysis of data) for describing information extracted from biological signals and applies it to respiratory data.
Journal ArticleDOI
Signal Processing for Nondifferentiable Data Defined on Cantor Sets: A Local Fractional Fourier Series Approach
TL;DR: In this paper, the local fractional Fourier series (LFFS) is used to process the signals, which are the LFFS continuous functions, and the results can be observed as significant extensions of the previously known results for the Fourier Series in the framework of the Local fractional calculus.
Journal ArticleDOI
Fluctuation Metrology Based on the Prony's Spectroscopy (II)
TL;DR: In this article, the Prony's spectroscopy is used to transform a wide class of multi-periodic and random signals (associated with a clearly expressed trend) to their amplitudefrequency response (AFR).
References
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Book
Introduction to Fourier Analysis on Euclidean Spaces.
Elias M. Stein,Guido Weiss +1 more
TL;DR: In this paper, the authors present a unified treatment of basic topics that arise in Fourier analysis, and illustrate the role played by the structure of Euclidean spaces, particularly the action of translations, dilatations, and rotations.
Journal ArticleDOI
Spectrum analysis—A modern perspective
Steven Kay,S.L. Marple +1 more
TL;DR: In this paper, a summary of many of the new techniques developed in the last two decades for spectrum analysis of discrete time series is presented, including classical periodogram, classical Blackman-Tukey, autoregressive (maximum entropy), moving average, autotegressive-moving average, maximum likelihood, Prony, and Pisarenko methods.
Book
An Introduction to Harmonic Analysis
TL;DR: In this article, the convergence of Fourier series on T and convergence of the conjugate function on T was studied, where T is the length of the line of a vector.