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.
Once you launch fltool, the main window appears. It is divided into four zones :
The pop-up menus allows to perform the various processings available in Fraclab. These are briefly described in sections 2.3 below and detailed in the corresponding parts of this help.
The basic elements one manipulates in Fraclab are structures: The synthesis and the analysis tools all produce and process structures. A structure is a composite piece of information which may comprise matrices of different size and other more complex elements. The upper middle part of the fltool graphic interface is composed of two windows : the Variables window, which will display the name of the structures generated in the course of using Fraclab. The highlighted name corresponds to the current active structure (i.e. the one on which the processings are made). The Details window shows the building blocks of the structure currently highlighted in the Variables window. To select a block, i.e. a sub-element of the structure (which may for instance be a matrix), just highlight it. This is useful for instance for purposes of visualization or if one wants to extract a particular building block from a composite structure.
Scan Workspace allows you to transfer files from your matlab environment (workspace) into the fltool environment, while Load allows you to transfer files from your file system into the fltool environment. Files formats that are currently recognized include mat-files, 1D ASCII signals and 2D tif images. Save allows you to save structures from fltool into your file system. Finally, Clear removes structures from both the fltool and the matlab environment.
View: This important menu allows to perform various display-related operations which are detailed below.
Help lists most of the routines available in Fraclab. To get a detailed help on a particular function, double click on it.
Quit is what you guess.
Finally, you may want to check the Message zone often, as error messages are usually displayed here. In many occasions, a beep is heard when a new message is sent. The Erase button lets you clear the message zone.
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.
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, ...
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.
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.
TF-TS allows to compute various time frequency representations of a signal, while misc offers basic structure manipulations such as sums, extractions, ...