Long term memory has frequently been observed in physical time series. Statistical theory for long term memory stochastic processes is radically different from the standard time series analysis, which assumes short term memory. The Allen variance is a particular measure of variability developed for long term memory processes. This variance can be interpreted as a Haar wavelet coefficient varian...

ABSTRACT: This paper begins by using the Haar wavelet to analyze the cumulative distribution function of a stream of two-valued Bernoulli trials. We find that this function maps binary numbers in [0,1] into non-uniform binary numbers in [0,1]. More generally, for r-valued Bernoulli trials, the distribution function likewise maps usual base-r numbers into non-uniform base-r numbers. We also find...

In order to get an efficient image representation we introduce a new adaptive Haar wavelet transform, called Tetrolet Transform. Tetrolets are Haar-type wavelets whose supports are tetrominoes which are shapes made by connecting four equal-sized squares. The corresponding filter bank algorithm is simple but enormously effective. In every level of the filter bank algorithm we divide the low-pass...

Internet has connected different parts of the world through a network link. Researchers in bioinformatics and biology have always wanted to share information for the progress of their research. But the data, they wanted to transfer are large-scale data sets which cannot be transferred over the existing network link in a considerable amount of time. Hence, methods to compress these large volumes...

Abstract: In this paper, identification of a continuous-time linear time-varying (LTV) system is proposed, where Haar wavelet with unit energy is employed. For that purpose, an algebraic equation is derived by expanding the input-output data and the time-varying impulse response using normalized Haar wavelets. Unknown wavelet coefficients for the a LTV system’s impulse response can be effective...

We compare two state-of-the-art non-linear techniques for nonparametric function estimation via piecewise constant approximation: the taut string and the Unbalanced Haar methods. While it is well-known that the latter is multiscale, it is not obvious that the former can also be interpreted as multiscale. We provide a unified multiscale representation for both methods, which offers an insight in...

In this paper, the Legendre wavelet method for State analysis of time-varying singular nonlinear systems is studied. The properties of Legendre wavelets and its operational matrices are first presented and then are used to convert into algebraic equations. Also the convergence and error analysis for the proposed technique have been discussed. Illustrative examples have been given to demonstrate...

A sequence of increasing translation invariant subspaces can be defined by the Haar-system (or generally by wavelets). The orthogonal projection to the subspaces generates a decomposition (multiresolution) of a signal. Regarding the rate of convergence and the number of operations, this kind of decomposition is much more favorable then the conventional Fourier expansion. In this paper, starting...

In this paper we present a comparative study on fusion of visual and thermal images using different wavelet transformations. Here, coefficients of discrete wavelet transforms from both visual and thermal images are computed separately and combined. Next, inverse discrete wavelet transformation is taken in order to obtain fused face image. Both Haar and Daubechies (db2) wavelet transforms have b...