Search results for "wavelet transform."
showing 10 items of 144 documents
Kolmogorov superposition theorem for image compression
2012
International audience; The authors present a novel approach for image compression based on an unconventional representation of images. The proposed approach is different from most of the existing techniques in the literature because the compression is not directly performed on the image pixels, but is rather applied to an equivalent monovariate representation of the wavelet-transformed image. More precisely, the authors have considered an adaptation of Kolmogorov superposition theorem proposed by Igelnik and known as the Kolmogorov spline network (KSN), in which the image is approximated by sums and compositions of specific monovariate functions. Using this representation, the authors trad…
Non-periodic Discrete-Spline Wavelets
2015
This chapter describes wavelet analysis in the spaces of discrete splines whose spans are powers of 2. This wavelet analysis is similar to wavelet analysis in the polynomial-spline spaces. The transforms are based on relations between exponential discrete splines from different resolution scales. Generators of discrete-spline wavelet spaces are described. The discrete-spline wavelet transforms generate wavelet transforms in signal space. Practically, wavelet transforms of signals are implemented by multirate filtering of signals by two-channel filter banks with the downsampling factor 2 (critically sampled filter banks). The filtering implementation is accelerated by switching to the polyph…
A computational method to optimal control of a wind turbine system using wavelets
2011
Author's version of a chapter in the book: Proceedings of the IEEE International Syposium on Computer-Aided Control System Design (2011). Also avaliable from the publisher at: http://dx.doi.org/10.1109/CACSD.2011.6044551 This paper deals with a computational optimization approach to the problem of state-feedback control design for a wind turbine system. The first step of the study is to develop a reduced order model for the system by considering the most important physical phenomena of aerodynamics and structural dynamics. Moreover, the behavior of the system can be influenced by the coupled dynamics between the tower motions and the blade pitch and turbine speed which can cause instabiliti…
A wavelet Methodology for EEG Time-frequency Analysis in a Time Discrimination Task
2009
EEG signals recorded by surface electrodes placed on the scalp can be thought as non- stationary stochastic processes in both time and space, especially in response to external stimuli. Cognitive tasks, in particular, are reflected by changes in EEG dynamics concerning both rhythms energy and connectivity across different brain regions. In the frequency-domain, EEG analysis is complicated and time-frequency methodologies are needed. The Wavelet Transform, in particular, represents a powerful tool for analysing, within a time-frequency embedding, the EEG. In this study we applied a wavelet-based methodology to extract quantitative time-frequency parameters from EEG signals recorded during a …
Prefiltering for pattern recognition using wavelet transform and neural networks
2003
Publisher Summary Neural networks are built from simple units interlinked by a set of weighted connections. Generally, these units are organized in layers. Each unit of the first layer (input layer) corresponds to a feature of a pattern that is to be analyzed. The units of the last layer (output layer) produce a decision after the propagation of information. Before feeding the computational data to neural networks, the signal must undergo a preprocessing in order to (1) define the initial transformation to represent the measured signal, (2) retain important features for class discrimination and discard that is irrelevant, and (3) reduce the volume of data to be processed, for example, data …
Time-Frequency behaviour of the a-wave of the human electroretinogram
2007
The electroretinogram is the record of the electrical response of the retina to a light stimulus. The two main components are the a-wave and the b-wave, the former is related to the early photoreceptoral activity. Aim of this paper is to acquire useful information about the time-frequency features of the human a-wave, by means of the wavelet analysis. This represents a proper approach in dealing with nonstationary signals. We have used the Mexican Hat as mother wavelet. The analysis, carried out for four representative values of the luminance, comprehends the frequency dependence of the variance and the skeleton. The results indicate a predominance of low frequency components, their time di…
Wavelet data analysis of EXAFS spectra
2009
Abstract The application of wavelet transform to the analysis of the extended X-ray absorption fine structure (EXAFS) from perovskite-type compounds is presented on the example of the Re L 3 -edge in ReO 3 and Co K-edge in LaCoO 3 . We propose a modified wavelet transform procedure, which allows better discrimination of the overlapped contributions into the EXAFS signal.
Polynomial Spline-Wavelets
2015
This chapter presents wavelets in the spaces of polynomial splines. The wavelets’ design is based on the Zak transform, which provides an integral representation of spline-wavelets. The exponential wavelets which participate in the integral representation are counterparts of the exponential splines that were introduced in Chap. 4. Fast algorithms for the wavelet transforms of splines are presented. Generators of spline-wavelet spaces are described, such as the B-wavelets and their duals and the Battle-Lemarie wavelets whose shifts form orthonormal bases of the spline-wavelet spaces.
Kolmogorov Superposition Theorem and Wavelet Decomposition for Image Compression
2009
International audience; Kolmogorov Superposition Theorem stands that any multivariate function can be decomposed into two types of monovariate functions that are called inner and external functions: each inner function is associated to one dimension and linearly combined to construct a hash-function that associates every point of a multidimensional space to a value of the real interval $[0,1]$. These intermediate values are then associated by external functions to the corresponding value of the multidimensional function. Thanks to the decomposition into monovariate functions, our goal is to apply this decomposition to images and obtain image compression. We propose a new algorithm to decomp…
Automatic detection of P, QRS and T patterns in 12 leads ECG signal based on CWT
2016
International audience; In this paper, a new method based on the continuous wavelet transform is described in order to detect the QRS, P and T waves. QRS, P and T waves may be distinguished from noise, baseline drift or irregular heartbeats. The algorithm, described in this paper, has been evaluated using the Computers in Cardiology (CinC) Challenge 2011 database and also applied on the MIT-BIH Arrhythmia database (MITDB). The data from the CinC Challenge 2011 are standard 12 ECG leads recordings with full diagnostic bandwidth compared to the MITDB which only includes two leads for each ECG signal. Firstly, our algorithm is validated using fifty 12 leads ECG samples from the CinC collection…