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2. Description of Fraclab Functionalities

2.1 Introduction

Fraclab can be approached from three different perspectives : synthesis of fractal signals, fractal analysis, and signal processing. This separation is artificial in a sense, since the tools associated with these three streams overlap greatly, but it is conceptually helpful. Most functionalities can be accessed either from a fractal analysis or from a signal processing point of view, and this help file will reflect this situation.

In order to make Fraclab user-friendly, a graphic interface, called fltool, is provided with this version. We describe briefly in the next sections the general organization of fltool, as well as the main features of the synthesis, analysis and signal processing tools, as they appear in the menus of fltool.

2.2 The main window of fltool

Once you launch fltool, the main window appears. It is divided into four zones :

2.3 Pop-up Menus Description

There are four kinds of pop-up menus : the first one allows to perform synthesis of "fractal" signals. The second one deals with the fractal and multifractal analysis of signals and includes : Fractional Dimensions, 1D Exponents Estimation, 1D signals Multifractal Spectra, and Stable Motion. The third group is related to Signal Processing and is composed of Segmentation and Denoising. Finally, miscellaneous tools are available, namely Time Frequency and Time Scale analysis and Misc, which allows to perform various editing tasks. Let us describe briefly what can be done with these various menus. More detailed explanations are given in the appropriate sections of this help.

Synthesis

Two types of signals can be generated : measures (i.e. an array of non negative data that add to one) or functions. Measures are interesting in particular when one needs to take into account the resolution in an explicit way. For both measures and signals, either deterministic or stochastic data may be generated. By and large, this menu allows to synthesize a substantial subset of all classical fractal models described in the literature : 1D and 2D fBm-s, mBm-s, (generalized) Weierstrass functions, stable motions, Wavelet based 1/f process, multifractal measures, ...

Fractal and Multifractal Analysis

The most basic parameters that can be computed are of course fractional dimensions. In the current implementation of Fraclab, only the box and regularization dimension are available. When one needs a local characterization of the signal, Hölder exponents are more pertinent, and the menu 1D Exponents Estimation allows to estimate both pointwise and local exponents. In addition, a long range exponent may be computed, as well as 2-microlocal exponents. 1D signals Multifractal Spectra offers various estimations procedures. Note that the computation of Multifractal Spectra for 2D data is possible using the Segmentation menu. Finally, Stable Motion allows to test the stability of a given process and to estimate the relevant parameters.

Signal Processing

Segmentation allows to segment both 1D signals and images. In the former case, a modeling based on a generalization of IFS, called weakly self affine functions, is used. Images are segmented into edges or regions of given regularity through multifractal analysis. Denoising allows to regularize and denoise 1D or 2D data using various methods.

Miscellaneous tools

TF-TS allows to compute various time frequency representations of a signal, while misc offers basic structure manipulations such as sums, extractions, ...


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