In this paper, we introduce an efficient method based on Haar wavelet to approximate a solutionfor the two-dimensional linear stochastic Fredholm integral equation. We also give an example to demonstrate the accuracy of the method.  

In order to extract the intrinsic information of climatic time series from background red noise, we will first give an analytic formula on the distribution of Haar wavelet power spectra of red noise in a rigorous statistical framework. The relation between scale aand Fourier period T for the Morlet wavelet is a= 0.97T . However, for Haar wavelet, the corresponding formula is a= 0.37T . Since fo...

In our previous work, we showed empirically that independent (Haar) wavelet models were parsimonious, computationally efficient and accurate in modeling heterogeneous network traffic measured by both auto-covariance functions and buffer loss rate. We also proved analytically that such models were capable of capturing any decay rate of auto-covariance functions at large lags. But the simplicity ...

The purpose is to study qualitative and quantitative rates of image compression by using different Haar wavelet banks. The experimental results of adaptive compression are provided. The paper deals with specific examples of orthogonal Haar bases generated by multiresolution analysis. Bases consist of three piecewise constant wavelet functions with a support $[0,1] \times [0,1] $.

Metode Wavelet merupakan salah satu metode yang unggul untuk menganalisis serta mengekstraksi ciri isyarat suara tutur. Dalam proses ekstraksi menggunakan Wavelet, terdapat beberapa faktor dapat berpengaruh dalam mendapatkan bersifat diskriminan, diantaranya: pemilihan mother wavelet, sub-band, dan level dekomposisi. Beberapa contoh sering digunakan Daubechies, Coiflet, Meyer, Haar, Symlet, Bio...

An orthogonal Haar scattering transform is a deep network computed with a hierarchy of additions, subtractions and absolute values over pairs of coefficients. Unsupervised learning optimizes Haar pairs to obtain sparse representations of training data with an algorithm of polynomial complexity. For signals defined on a graph, a Haar scattering is computed by cascading orthogonal Haar wavelet tr...

It is well known that the Haar and Shannon wavelets in L2(R) are at opposite extremes, in the sense that the Haar wavelet is localized in time but not in frequency, whereas the Shannon wavelet is localized in freqency but not in time. We present a rich setting where the Haar and Shannon wavelets coincide and are localized both in time and in frequency. More generally, if R is replaced by a grou...

A modification of the Haar wavelet method, for which the stepsize of the argument is variable, is proposed. To establish the efficiency of the method three test problems, for which exact solution is known, are considered. Computer simulations show clear preference of the suggested method compared with the Haar wavelet method of a constant stepsize. 2007 Elsevier Inc. All rights reserved.

Recently, we have been developing general multireso-lution signal decomposition schemes that unify traditional (linear) approaches and allow use of nonlinear ltering techniques in the decomposition. This paper summarizes our approach and provides several simple examples. Some of these examples are known in the literature (e.g., Haar pyramid and wavelet) and some of them are new (e.g., morpholog...