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001432994 001__ 1432994
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001432994 019__ $$a1227059139$$a1228650637$$a1232856089$$a1238201850
001432994 020__ $$a9783030626723$$q(electronic bk.)
001432994 020__ $$a3030626725$$q(electronic bk.)
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001432994 0247_ $$a10.1007/978-3-030-62672-3$$2doi
001432994 035__ $$aSP(OCoLC)1227391171
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001432994 1001_ $$aBanerjee, Santo,$$d1976-
001432994 24510 $$aFractal functions, dimensions and signal analysis /$$cSanto Banerjee, D. Easwaramoorthy, A. Gowrisankar.
001432994 260__ $$aCham :$$bSpringer,$$c2021.
001432994 300__ $$a1 online resource (140 pages)
001432994 336__ $$atext$$btxt$$2rdacontent
001432994 337__ $$acomputer$$bc$$2rdamedia
001432994 338__ $$aonline resource$$bcr$$2rdacarrier
001432994 347__ $$atext file
001432994 347__ $$bPDF
001432994 4901_ $$aUnderstanding Complex Systems
001432994 5050_ $$aIntro -- Preface -- Contents -- 1 Mathematical Background of Deterministic Fractals -- 1.1 Introduction -- 1.2 Iterated Function System -- 1.3 Countable Iterated Function System -- 1.4 Local Countable Iterated Function System -- 1.4.1 Local Iterated Function System -- 1.4.2 Existence and Analytical Properties of LCIFS -- 1.5 Fractal Dimension -- 1.6 Generalized Fractal Dimensions -- 1.6.1 Some Special Cases -- 1.6.2 Limiting Cases of Generalized Fractal Dimensions -- 1.6.3 Range of Generalized Fractal Dimensions -- 1.7 Concluding Remarks -- 2 Fractal Functions -- 2.1 Introduction
001432994 5058_ $$a2.2 Interpolation Functions -- 2.3 Fractal Interpolation Function -- 2.4 Hidden Variable Fractal Interpolation Function -- 2.5 Classical Calculus on Fractal Interpolation Functions -- 2.6 Concluding Remarks -- 3 Fractional Calculus on Fractal Functions -- 3.1 Introduction -- 3.2 Linear Fractal Interpolation Function -- 3.3 Riemann-Liouville Fractional Calculus Quadratic FIF -- 3.4 Fractal Dimension -- 3.5 Fractional Calculus of Quadratic FIF with Variable Scaling Factors -- 3.6 Concluding Remarks -- 4 Fractal Interpolation Function for Countable Data -- 4.1 Introduction
001432994 5058_ $$a4.2 Existence of FIF for Countable Data Set -- 4.3 Fractional Calculus on Interpolation Function of Sequence of Data -- 4.4 Concluding Remarks -- 5 Multifractal Analysis and Wavelet Decomposition in EEG Signal Classification -- 5.1 Introduction -- 5.2 Experimental Signals -- 5.2.1 Synthetic Weierstrass Signals -- 5.2.2 Clinical EEG Signals -- 5.3 Statistical Methods -- 5.3.1 ANOVA Test -- 5.3.2 Box Plot -- 5.3.3 Normal Probability Plot -- 5.4 Development of Multifractal Analysis in EEG Signal Classification -- 5.4.1 Modified Generalized Fractal Dimensions
001432994 5058_ $$a5.4.2 Improved Generalized Fractal Dimensions -- 5.4.3 Advanced Generalized Fractal Dimensions -- 5.4.4 Methods to Analyze the Fractal Time Signals -- 5.4.5 Results and Discussions -- 5.5 Multifractal-Wavelet Based Denoising in EEG Signal Classification -- 5.5.1 Discrete Wavelet Transform -- 5.5.2 Wavelet Denoising of Signals -- 5.5.3 Results and Discussions -- 5.6 Concluding Remarks -- 6 Fuzzy Multifractal Analysis in ECG Signal Classification -- 6.1 Introduction -- 6.2 Fuzzy Multifractal Analysis for Fractal Signals -- 6.2.1 Fuzzy Renyi Entropy
001432994 5058_ $$a6.2.2 Fuzzy Generalized Fractal Dimensions for Signals -- 6.3 Fuzzy Generalized Fractal Dimensions for Deterministic Fractal Waveforms -- 6.4 Experimental ECG Data -- 6.5 Fuzzy Generalized Fractal Dimensions for Clinical ECG Signals -- 6.6 Concluding Remarks -- Appendix References
001432994 506__ $$aAccess limited to authorized users.
001432994 520__ $$aThis book introduces the fractal interpolation functions (FIFs) in approximation theory to the readers and the concerned researchers in advanced level. FIFs can be used to precisely reconstruct the naturally occurring functions when compared with the classical interpolants. The book focuses on the construction of fractals in metric space through various iterated function systems. It begins by providing the Mathematical background behind the fractal interpolation functions with its graphical representations and then introduces the fractional integral and fractional derivative on fractal functions in various scenarios. Further, the existence of the fractal interpolation function with the countable iterated function system is demonstrated by taking suitable monotone and bounded sequences. It also covers the dimension of fractal functions and investigates the relationship between the fractal dimension and the fractional order of fractal interpolation functions. Moreover, this book explores the idea of fractal interpolation in the reconstruction scheme of illustrative waveforms and discusses the problems of identification of the characterizing parameters. In the application section, this research compendium addresses the signal processing and its Mathematical methodologies. A wavelet-based denoising method for the recovery of electroencephalogram (EEG) signals contaminated by nonstationary noises is presented, and the author investigates the recognition of healthy, epileptic EEG and cardiac ECG signals using multifractal measures. This book is intended for professionals in the field of Mathematics, Physics and Computer Science, helping them broaden their understanding of fractal functions and dimensions, while also providing the illustrative experimental applications for researchers in biomedicine and neuroscience.
001432994 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed February 18, 2021).
001432994 650_0 $$aInterpolation.
001432994 650_0 $$aFractals.
001432994 650_0 $$aStatistical physics.
001432994 650_0 $$aComputational complexity.
001432994 650_0 $$aSystem theory.
001432994 650_6 $$aInterpolation.
001432994 650_6 $$aFractales.
001432994 650_6 $$aPhysique statistique.
001432994 650_6 $$aComplexité de calcul (Informatique)
001432994 650_6 $$aThéorie des systèmes.
001432994 655_0 $$aElectronic books.
001432994 7001_ $$aEaswaramoorthy, D.
001432994 7001_ $$aGowrisankar, A.$$q(Arulprakash)
001432994 77608 $$iPrint version:$$aBanerjee, Santo.$$tFractal Functions, Dimensions and Signal Analysis.$$dCham : Springer International Publishing AG, ©2021$$z9783030626716
001432994 830_0 $$aUnderstanding complex systems.
001432994 852__ $$bebk
001432994 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-62672-3$$zOnline Access$$91397441.1
001432994 909CO $$ooai:library.usi.edu:1432994$$pGLOBAL_SET
001432994 980__ $$aBIB
001432994 980__ $$aEBOOK
001432994 982__ $$aEbook
001432994 983__ $$aOnline
001432994 994__ $$a92$$bISE