Jul 31, 2006 · Isotropic and Anisotropic FEXP-Fractal Spectral Models for High Resolution Sea SAR Images Mar 9, 2017 · Chatter is a kind of self-excited unstable vibration during machining process, which always leads to multiple negative effects such as poor surface quality, dimension accuracy error, excessive noise, and tool wear. However, by transferring self-similar measures on IR" to M via local coordinates we easily obtain abundant examples of measures on M that satisfy both (1. Chun-Kit Lai, Yang Wang, Non-spectral fractal measures with Fourier frames. We report . Aug 1, 2009 · More formally, Mandelbrot (1983) defined a fractal set as a set for which the Hausdorff dimension (D h) is greater than its topological dimension (D T). Nine different fractal dimension values (D) with an increment of 0. 63, and its fractal dimension in y direction is 1. We give several examples illustrating this and a simple argument, based on surface fragility, for why the Jan 1, 2021 · The Journal of Fractal Geometry is dedicated to publishing high quality contributions to fractal geometry and related subjects, or to mathematics in areas where fractal properties play an important role. May 18, 2022 · Methods: In this study, the SPAD value was predicted by calculating the spectral fractal dimension index (SFDI) from a hyperspectral curve (420 to 950 nm). The amplitude spectrum of source magnetization is proportional to the wavenumber (k) raised to a fractal exponent (-β). The two-dimensional discrete Fourier transform The discrete Fourier transform (DFT) of a two-dimensional dataset z(x,y) consisting of N x ×N y measure-ments spaced at even intervals Δx and Δy can be written [Priestley, 1981; Percival and Walden, 1993] Z(k x,k y)= N x−1 m=0 1 Introduction The fractional Brownian motion (fBm) is a continuous-time Gaussian process that gener-alises the standard Brownian motion. Although a relationship between these measures has been derived mathematically, empirical validation across measurements is lacking. 2. range of 7–16 km in the Zagros, east Alborz, Tabas, Jazmurian and Makran regions, sho wing a. In pink noise, each octave interval (halving or doubling in frequency) carries an equal amount of noise energy. The wave-spectrum scaling methods can be applied to both self-similar fractal signals and self-affine fractal signals in the geographical world. Both are not important for D =1. [ 28 ]. 1. Methods 2. Jan 25, 2016 · New Zealand-based Lectro Spektral Daze returns to Neogoa Records, this time to present his new album, Full Fractal Vision. Here, we present a new method, namely the irregular-resampling auto-spectral analysis (IRASA), to separate fractal and oscillatory components in the power spectrum of neurophysiological signal according to their Aug 6, 2002 · The one parameter of this function is the fractal dimension, and it can be estimated directly from an autocorrelogram (correlation analysis). This study explores extant electroencephalogram (EEG) signals in search of patterns that could differentiate subjects undertaking mental tasks and reveals insights on said data. In this method, we irregularly resampled the neural signal by a set of non-integer Mar 7, 2023 · We propose both a probabilistic fractal model and fractal dimension estimator for multi-spectral images. g. Conclusions. 1 are varied from 0. Mar 15, 2022 · The present work develops a model for the turbulent velocity spectra that considers the anomalous behaviour of the turbulent flow. close correlation with depths estimated from the maximum May 1, 2016 · This study has mainly presented an overview of fractal/multifractal models used to model geochemical data. In the application of conventional audio compression algorithms to low bit rate audio coding one is faced with May 20, 2021 · fractal surface looks the same when part of the surface is magnified. It is thus natural to ask Secondly, if one computes not only the fractal cross-spectral power between x(t) and y(t) but also their fractal and oscillatory spectra separately with IRASA, the remaining confounding interaction terms from |SS XY (ùù)| 2 can also be eliminated and thus a theoretically unbiased estimate of oscillatory cross-spectral power can also be Sep 4, 2006 · A fractal relief model is used as a basis for creating simulated SAR pictures. 5. Firstly, analytical spectral devices (ASD) were used to measure the hyperspectral curves of different Feb 15, 2014 · The spectral-theoretic and geometric properties we have previously established for U are as follows: (i) U acts as an ergodic operator; (ii) the action of U is not spatial; and finally, (iii) U is fractal in the sense that it is unitarily equivalent to a countable infinite direct sum of (twisted) copies of itself. Thus, a power spectrum Fractal AC Circuits and Propagating Waves on Fractals (Eric Akkermans, Joe P Chen, Gerald Dunne, Luke G Rogers and Alexander Teplyaev) Readership: Academic mathematicians and physicists, both pure and applied, working on fractals or rough spaces or interested in fractal media; Scientists from the many areas in which fractal models are important Dec 1, 2005 · Transmission spectra of one-dimensional fractal multilayer structures are found to exhibit self-similar properties. Oct 15, 2012 · As a consequence of the power law, the plot in a log–log scale of the graph of F h x f results in a curve whose behavior approximates that of a straight line. This process was shown useful in characterising the Mar 7, 2014 · Abstract. Moreover, the roughness parameters of self-affine fractal surfaces, such as the root-mean-square roughness and average surface curvature, are related to the measurement length scale. The characteristics of fractal rough surfaces simulated by the spectral representation method and the Jul 6, 2022 · Abstract The paper delineates a novel method based on power spectral fractal dimension for the identification, classification, and prediction of normal, benign, and malignant regions in a mammogram. In this model, an earthquake is composed of a hierarchical set of smaller earthquakes. Measuring fractal dimension Fractal dimension, which can be the characteristic measurement of mainly the structure of an object in a digital image [19], [16], [4], [1], can be computed applying the Box counting as follows: 1. To estimate the shape of sedimentary basins, a critical parameter in hydrocarbon exploration, we calculated the depth of magnetic basement by applying a fractal spectral method to the aeromagnetic map of Iran. The fractal method of the Allan Factor applied to the series of Jul 1, 1997 · Application of fractal theory to quantify the roughness of rock fractures has been well developed, and various methods have been presented to estimate the fractal dimension of roughness profiles, D. Fractal Geom. Many unexpected prop erties of the F ourier bases were discov-ered [St2, DHS, DaHL]. The fractal dimension is widely used to characterise the surface texture and statistical index of fractal properties of thin films and other textures [ 38 ]. In 1981, Hutchinson showed that for each iterated function system {τ1, …, τn } on [0, 1], there exists a unique probability measure, called a Hutchinson measure or fractal measure, whose Aug 1, 2022 · The fractal characteristics of the statistical surface and machined surface with different nominal roughness are investigated. Linear SASI method is based on evaluation of the balance of powers in two EEG frequency bands in one channel selected higher and lower than the alpha band Feb 10, 2014 · 1 4 . The man behind this project, Danny Marshall, is a hard-working guy who always delivers something new and interesting and this one our results for fractal descriptions of landscapes. For example, it varies by voluntary eyes opening and closing in terms of the broadband power and the power-law exponent (Fig. However, such spatial analyses generally are not well-suited for the analysis of so-called “time-series Sep 23, 2015 · Non-spectral fractal measures with Fourier frames. Apr 10, 1991 · I assume that the high frequency energy of a main shock is produced by a self-similar distribution of subevents, where the number of subevents with radii greater than R is proportional to R −D, D being the fractal dimension. The model is validated mathematically under the assumption of statistical independence of the spectral components. The correlation between the SPAD value and hyperspectral information was further analyzed for determining the sensitive bands that correspond to different disease levels. 9. 237 (8) 238 totics of eigenvalues, remainder estimate, Weyl-Berry conjecture, fractals, Minkowski and Hausdorff dimensions, vibrations of fractal drums, spectral and fractal geometry. The model is based on the widely known fractional Brownian motion fractal model, which is extended to the case of images with multiple spectral bands. 585, and the dimension obtained from network perspective is 1. The fractal dynamics, as the broadband activity underneath neural oscillations, fluctuates over time in a way that seems functionally relevant. Introduction. We generalize the compatible tower condition given by Strichartz to the almost-Parseval-frame tower and show that non-trivial examples of almost-Parseval-frame tower exist. like a Sep 12, 2017 · Cite this article. The relief aspect is controlled by the filter shape. fractal dimension can be applied to the measured data. some results concerning the spectral dimension of Laplacians defined by fractal Nov 20, 2018 · Many methods exist for quantifying the fractal characteristics of a structure via a fractal dimension. Fractal is an appropriate mathematical tool, and fractal dimension can be used to explain the comprehensive variation of a curve. The main goal of this project is to provide a simple but flexible framework for creating graph neural networks (GNNs). 1994). Jul 19, 2016 · The fractal dimension is calculated from a DEM, and the methodology proposed here is to calculate the fractal dimension inside a moving window (Taud and Parrot, 2005), thus assessing the local Spectral Properties of Laplacians Defined by Fractal Measures Abstract The spectral dimension of a fractal Laplacian is a fundamental quantity that plays an important role in studying the analytic properties of the operator. China Dec 28, 2009 · In the present publication the so far well known algorithms calculating fractal dimension in a simple way will be introduced (CISSE SCSS 2005), [6] as well as the new mathematical concept named by the author ‘Spectral Fractal Dimension - SFD’. The reconstructed result not only augments the data points to improve the statistics but also retains the turbulent fractal dimension of the flow. Stationary fractal processes with finite long memory can be modeled with 0 < d < 0. The major benefit of the fractal dimension is its sensitivity to changes of the spectral information, caused by the geometric configuration, shape, reflectance, etc. 4 (2017), no. The application of the spectral representation method in generating Gaussian and non-Gaussian fractal rough surfaces is studied in this work. In this paper, a fast and accurate fractal parameters estimation method, called FPENN, was proposed in a global D interval to improve rough surface topography recognition and contact mechanics. These results demonstrate the efficacy and potential applications of this method in analyzing electrophysiological signatures of large-scale neural circuit activity. Many unexpected properties of the Fourier bases were discov-ered [St2, DHS, DaHL]. Nov 23, 2020 · Using the fractal parameters, we can make spatial analyses for the geographical signals. 15\). Nov 19, 2021 · groups can be identified from the fractal measures calculated fr om the EEG activity dataset. We say that a compactly supported probability measure μ is a spectral measure if there exists a set of complex exponentials E ( Λ): = { e 2 π i 〈 λ, x 〉 } λ ∈ Λ such that it is an orthonormal basis of L 2 ( μ). In this paper, we show that fractal exponent and Curie depth are so strongly inter-connected that attempts to simultaneous or Apr 1, 2000 · Since statistical parameters are instrument-dependent, Majumdar and Bhushan [6] developed a fractal model for elastic–plastic contact between rough surfaces, based on fractal geometry. 22 It also determines how the fractal differs from Euclidean objects. Sep 30, 2014 · The fractal dimension (D) is a global scaling property to characterize fractal patterns or sets by quantifying their complexity as well as a statistical measure that correlates the morphological structural complexity of cellular components and biological tissues. However, determination of D is still a challenging issue, and researchers have attributed different values to fractal dimensions of the standard Oct 1, 2001 · For large fractal dimension (e. 1 Measuring fractal dimension. And spectral density from 10 3 π to infinity is important for D =1. The size of the gap is expressed using the additive energy of stereographic projections of the limit set. , D =1. The line scaling The temporal fluctuation in the broadband power of the fractal compo- nent revealed characteristic dynamics within and across the eyes-closed, eyes-open and sleep states. Here, we present a new method, namely the irregular-resampling auto-spectral analysis (IRASA), to separate fractal and oscillatory components in the power spectrum of neurophysiological signal according to their distinct temporal and spectral characteristics. Aug 18, 2016 · We obtain an essential spectral gap for n-dimensional convex co-compact hyperbolic manifolds with the dimension $${\\delta}$$ δ of the limit set close to $${{n-1\\over 2}}$$ n - 1 2 . Aug 10, 2019 · As an independent geothermal proxy, the Curie-point depth has important geodynamic implications, but its estimation from magnetic anomalies requires an understanding of the spatial correlation of source magnetization, mathematically characterized by a fractal exponent. Spektral is a Python library for graph deep learning, based on the Keras API and TensorFlow 2. The “range” is of the integral of deviations Oct 25, 2023 · The time dynamics of the instrumental seismicity recorded in the area of the Lai Chau reservoir (Vietnam) between 2015 and 2021 were analyzed in this study. 2. With these assumptions, we can parametrize the magnetization of a given slab by the depth to the top of the Sep 2, 2011 · Fractal analysis reveals that the changes of amplitude coefficient and curve length of the profiles are the main contribution to the loss of friction. We then define the unitary operator U in L 2 (μ) from a scale-by-5 operation. (4), the profile spectral densities can be obtained. The solution of the DO-FBTE is approximated by a truncated series of shifted Sep 1, 2021 · The Sierpinski triangle network shown in Fig. Jul 15, 2017 · Spectra. Let km = m and kn = n for m =0, 1,…, N −1 and n =0, 1,…, N −1 be spatial frequencies. The Gutenberg–Richter analysis of the frequency–magnitude distribution has revealed that the seismic catalog is complete for events with magnitudes larger or equal to 0. Power Spectrum digital fractal signals Hybrid Methods calculate the fractal dimension of 2D using 1D methods III. The general form of the model is shown in Equation (2), where A(ρ) denotes the area with concentration values greater than the contour Dec 11, 2005 · Fractal analysis of digital images is of great value, for instance, in Medicine [1][2][3][4][5]or Botanics [6, 7] and for the characterization of many other physical processes [8, 9]. DOI 10. 1 is a classical fractal object, and its fractal dimension is the ratio of the number of new copies to the scaling of new copies. 2, kx =1, ky =4. Jorgensen, S. Here, we determine the relationship between D and β for 1- and 2-dimensional fractals. Nov 16, 2021 · The fractal dimension of 420-950 nm bands, , is fitted by the logarithmic of Hausdorff dimens ion 236 [43] and the formula is defined in Eq uation (8 ). Its fractal dimension in x direction is 1. Analogous to the procedure followed in Section 4. Another statistical measure from which the fractal dimension can be calculated is Hurst’s rescaled range analysis [9, 10] for analyzing flows in rivers. The author's research was partially supported by the National Science Foundation under Grant DMS-8703138. Malignant lesions show a Nov 1, 2007 · 2. 8, Dy =1. 305–327. Oct 26, 2023 · One of the issues in numerical solution analysis is the non-linear distributed-order fractional Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. Using this model, we Sep 23, 2015 · Non-spectral fractal measures with Fourier frames. We estimated the power spectral density of May 15, 2023 · Authors and Affiliations. By doing so, we demonstrate the first singular fractal measure which has only finitely many mutually orthogonal Sep 7, 2022 · The fractal dimension propounds the order of any aspect of surface roughness, but it is now widely accepted that there is no precise definition for fractal dimensions [36, 37]. With: The Hausdorff–Besicovitch dimension D h is defined as the logarithmic ratio between the number N of an object’s internal homotheties and the reciprocal of the common ratio r of this homothety: (1) D h = ln (N) ln 1 r The homothety Apr 1, 2017 · A zero fractal parameter results in a white noise power spectrum of the magnetization field. Math. (1994) can be used to separate geochemical and geophysical anomalies from background values in order to characterize the distribution of elements in a study area. Its dimension is log 3 ∕ log 2 = 1. , polished or sandblasted surfaces, are self-affine fractal over a wide range of length scales, with the fractal dimension \ (D_ {\mathrm {f}} = 2. More specifically, I study the existence and structure of the exponential orthonormal bases, Fourier frames, Riesz basis, windowed exponentials on fractal measures. , before the addition of the sinusoidal components (denoted as raw). The spectral-theoretic and geometric properties we have previously established for U are as follows: (i) U acts as an ergodic operator; (ii) the action of U is not spatial; and finally, (iii) U is fractal in the sense that it is unitarily equivalent to a countable infinite direct sum of (twisted) copies of Pink noise, f noise, fractional noise or fractal noise is a signal or process with a frequency spectrum such that the power spectral density (power per frequency interval) is inversely proportional to the frequency of the signal. 3, pp. Oct 5, 2021 · In terms of generating fractal surfaces, they were first studied in simulating fractal images by Voss 26,27 and Saupe 28 in the 1980s. These models, including C-A, S-A, the singularity mapping technique, etc. Pink noise has d of 0. There were great expectations in the 1980s in connection with the practical applications of May 18, 2022 · A fractal dimension can be seen as a statistical index that characterizes patterns by quantifying the irregularity as a ratio of the change in detail to the change in scale. Mathematics. Law of Pure Types and Some Exotic Spectra of Fractal Spectral Measures Xin-Rong Dai, Xing-Gang He and Chun-Kit Lai Abstract Let μ be a Borel probability measure with compact support in Rd and Nov 6, 2023 · According to the literature, the utilization of spatial features can significantly enhance the accuracy of hyperspectral image (HSI) classification. Chun-Kit Lai, Yang Wang. We find that for 1-dimensional Nov 1, 2007 · In this paper, the well known algorithms calculating fractal dimension in a much simplified manner will be presented and the novel mathematical concepts, named by the author as 'Spectral Fractal Dimension' are also described. In order to compute dimension, the definition of spectral. Aug 29, 2015 · Neurophysiological field-potential signals consist of both arrhythmic and rhythmic patterns indicative of the fractal and oscillatory dynamics arising from likely distinct mechanisms. 2 ). side is only one (bit). Most natural surfaces and surfaces of engineering interest, e. We solve the problem by proposing a numerical solution based on the shifted Legendre Gauss–Lobatto (SL-GL) collocation technique. Russ [7] shows that the Fourier fractal dimension F D h of the image can be calculated by F D h = 6 + β h 2, where β h is the slope of the straight line best fitted to the curve in log–log scale. In the proposed method, the Nov 15, 1991 · FRACTAL MEASURES 179 Somewhat more precise results for self-similar measures on IR" are estab- lished in [S3, S4], but there is no analogue of self-similarity in the present context. For purposes of monitoring the processing state of milling process and detecting chatter timely, a novel online chatter detection method was proposed. This study was aimed to compare two electroencephalogram (EEG) analysis methods, spectral asymmetry index (SASI) and Higuchi's fractal dimension (HFD), for detection of depression. 8 4 1. Published in Journal of Fractal Geometry 23 September 2015. We first test whether long-wavelength components are . 36,37,39 There Spectral decimation for a graph-directed fractal pair Shiping Cao1,HuaQiu2,∗, Haoran Tian2 & Lijian Yang3 1Department of Mathematics, Cornell University, Ithaca, NY 14850, USA; 2Department of Mathematics, Nanjing University, Nanjing 210093,China; 3Department of Mathematics, University of Kansas, Lawrence, KS 66045, USA Aug 1, 2020 · Particularly, for some fractal networks [14,15], such as Koch networks [16], Vicsek fractals [1], Sierpiński graphs [17], are all good candidate network models to derive an exact scaling of Tiling theory. You can use Spektral for classifying the users of a social network, predicting molecular properties, generating Aug 2, 2014 · Jorgensen and Pedersen [P. It can be integrated into the models that are used for permeability prediction. The technique employed is bidimensional Fourier filtering. If α is obtained, the de-fractal process can be implemented on the observed spectrum through the multiplication of k α factor and the observed spectrum. If such Λ exists, it is called a spectrum of μ. Spectral analysis reveals that the polishing action play an important role in the changes of micro-texture. Nov 17, 2021 · Brain electrical activity recorded as electroencephalogram data provides relevant information that can contribute to a better understanding of pathologies and human behaviour. 4171/JFG/52 Therefore, instead of comparing the obtained cross-spectral slopes to their corresponding expected theoretical value, we computed the difference of mixed and fractal to the spectral exponent derived via MRCSA from the raw mixed-correlated ARFIMA time series pairs, i. 1 to 0. 5 ≤ d ≤ 1, the process is non-stationary. As such, the broadband fractal activity is at least not pure noise, and Mar 13, 2005 · Repeat steps 3-5 until one (the shortest) spectral. the box-counting method, the PSD method, the roughness-length method and the variogram method). Therefore, in the present study, fractal theory was used to analyze the healthy status of different vegetation. In HSI classification, textural features are typically extracted from dimensionally reduced data cubes, such as principal component analysis (PCA A new concept of feature size range of a roughness profile is introduced in the paper. We investigated the fractal dimension of the pore volume of 11 Eocene sandstone samples from China. 456, which is close to its dimension. 9 and 1000 profiles for each D are Oct 29, 2019 · k is the radial wave number and α is the fractal index of α = β − 1, in which β is referred to as the fractal parameter of magnetization (Maus and Dimri. There were great expectations in the 1980s in connection with the practical applications of mathematical processes which were built mainly upon the fractal dimension Mar 13, 2005 · In the present publication the so far well known algorithms calculating fractal dimension in a simple way will be introduced as well as the new mathematical concept named by the author 'spectral fractal Dimension', the algorithm derived from this concept and the possibilities of their practical usage. J. While Fourier analysis appears to work perfectly on fractal spectral measures, for the measures which are non-spectral, it is natural to ask the following question. The depth of magnetic basement is a close proxy for the shape of sedimentary basins provided that igneous basement is strongly magnetized relative to the overlying sediments and there is Sep 23, 2015 · the discovery, more fractal measures were found to b e spectral by many others [St1, LaW1, DJ1]. 4) and Oct 22, 2015 · The C-A fractal model proposed by Cheng et al. Spectral density from 0 to π is important for D =1. 6. [3] [9] Fractal dimensions are used to characterize a broad spectrum of Apr 1, 2017 · The depth of magnetic basement is in the. Anal. In their model, fractal surfaces can be characterized by two parameters: a non-integer fractal dimension D and a scale constant G. 9). 2–5 Most of the widely used roughness parameters are determined based on a dis- the discovery, more fractal measures were found to be spectral by many others [St1, L aW1, DJ1]. measurement of mainly the structure of an object in a. They proposed several methods, including the fast Fourier transform (FFT) filtering method, random midpoint displacement (RMD), successive random additions, and Weierstrass–Mandelbrot (W–M) random fractal An unequally spaced fractal interpolation method is developed to reconstruct the low data rate laser Doppler velocimetry (LDV) signal for better spectral results. That is, Dx =1. 15\pm 0. The Welcome to Spektral. 9), the spectral density at high wave number is important for structure function at short distance. Fractal dimension, which can be the characteristic. Self-similarity manifests itself in the shape of a transmission envelope (map of transmission dips) rather than in the map of resonance transmission peaks, as is commonly the case with spectra of quasiperiodic systems. By using Eq. , have been used widely to detect anomalies in geochemical exploration and determine the geochemical baseline in environmental studies. For 0. Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, P. The $$\\beta $$ β -model assumes that the standard Kolmogorov phenomenology is valid only in active turbulence regions, and it proposes an expression for the turbulent velocity spectra in the inertial subrange that is a function of the Hausdorff fractal dimension Jul 1, 2002 · If a weakly anisotropic fractal surface with surface spectral density, P (ω x ,ω y )= 1 ω x 2 + ω y 1. Frame theory. Many fractals are constructed as natural limits of certain sets with a simpler structure: for instance, the Sierpiński is the limit of finite graphs consisting of various affine images of an equilateral triangle. It is shown that this feature size range plays an important role in estimating the fractal dimension,D, accurately using the divider method. Discussions are given to indicate the difficulty of using both the divider and the box methods in estimatingD accurately for self-affine profiles. 75 (1998) 185-228] proved that if ρ = 1 / q where q is an even integer, then L 2 Oct 14, 2020 · Noncommutative geometry provides a framework, via the construction of spectral triples, for the study of the geometry of certain classes of fractals. Jul 19, 2016 · Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D) and power spectrum decay rate (β). Jan 1, 2010 · In order to study the fractal features of ITO thin films, the PSD (power spectral density) functions of all the surface profiles of each film have been calculated and combined in to a single PSD profile covering large spatial frequency bandwidth. As a traditional example, a fractal dimension of a spatial fractal structure may be quantified via a box-counting fractal analysis that probes a manner in which the structure fills space. digital image [15], [12], [4], [1], can be computed Jul 1, 2017 · The fractal dimension describes the size of the geometric objects as a function of resolution. For this, the fractal dimension values are found in the radial directions from a reference point and are used for classifying the regions, unlike conventional methods. 45. Pedersen, Dense analytic subspaces in fractal L 2-spaces, J. e. In other words, the interpolated data are flow turbulence-correlated data which are We estimate Curie-point depths (Z<SUB>b</SUB>) of the western United States and northeast Pacific Ocean by analyzing radially averaged amplitude spectra of magnetic anomalies based on a fractal magnetization model. Fractal features are powerful measures of texture, representing the local complexity of an image. It is concluded that the evolution of friction of aggregate is governed by micro fractal and spectral geometry with aspects of number theory [30, 31, 25, 26], the above spectral characterization of the Riemann hypothesis may shed new light on A fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale. The fractal parameter is related to the slope of the log-log plot of the magnetization power spectrum versus the norm of the wave number, k. , MDCT), based on a Fractal SelfSimilarity Model (FSSM) for the short-term frequency representation ofThe signal. ©1991 American Mathematical Society Jan 1, 2017 · The fractal dimension of the generated profiles is then extracted from the surfaces by four different methods (i. R. This study has implications for the further development of fractal-based spatiotemporal signal analysis in the May 7, 2012 · This enables ARFIMA-models to give parsimonious descriptions of any long-range dependencies in time series. 1 , we conducted a Shapiro–Wilk normality test [ May 1, 2005 · This paper describes one of a newer class of Frequency Extension techniques which are applied directly to the high frequency resolution representation of the signal (e. This additive energy can in turn be estimated in terms of the constants in Ahlfors–David regularity of Abstract. [5] : 1 Several types of fractal dimension can be measured theoretically and empirically ( see Fig. Because of its relation with applied harmonic analysis, I am also interested in classical sampling theory and Gabor analysis. Such topics include: The Journal of Fractal Geometry accepts submissions containing original research articles and short communications. 1. qm fe gu rc rj pf wq rf xy nx