This paper presents a rational Haar wavelet operational method for solving the inverse Laplace transform problem and improves inherent errors from irrational Haar wavelet. The approach is thus straightforward, rather simple and suitable for computer programming. We define that $P$ is the operational matrix for integration of the orthogonal Haar wavelet. Simultaneously, simplify the formulaes of...

This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.

In this paper, we present comparative analysis of scale-invariant feature extraction using different wavelet bases. The main advantage of the wavelet transform is the multi-resolution analysis. Furthermore, wavelets enable localization in both space and frequency domains and high-frequency salient feature detection. Wavelet transforms can use various basis functions. This research aims at compa...

The classical Haar wavelet system of L2(R) is commonly considered to be very local in space. We introduce and study in this paper piecewise-constant framelets (PCF) that include the Haar system as a special case. We show that any bi-framelet pair consisting of PCFs provides the same Besov space characterizations as the Haar system. In particular, it has Jackson-type performance sJ = 1 and Berns...

In this paper a new multivariate regression estimate is introduced. It is based on ideas derived in the context of wavelet estimates and is constructed by hard thresholding of estimates of coefficients of a series expansion of the regression function. Multivariate functions constructed analogously to the classical Haar wavelets are used for the series expansion. These functions are orthogonal i...

This paper presents a technique of digital image watermarking using DCT wavelet transform. Use of Haar wavelet is very common in watermarking. However, here DCT wavelet transform of size 256*256 is generated using existing well known orthogonal transform DCT of dimension 128*128 and 2*2. This DCT Wavelet transform is used in combination with the orthogonal transform DCT and SVD to increase the ...

We investigate the statistical properties of $C=uvu^{-1}v^{-1}$, when $u$ and $v$ are independent random matrices, uniformly distributed with respect to Haar measure groups $U(N)$ $O(N)$. An exact formula is derived for average value power sum symmetric functions $C$, also products matrix elements similar Weingarten functions. The density eigenvalues $C$ shown become constant in large-$N$ limit...

this paper presents a proof of stirling's formula using haar wavelets and some properties of hilbert space, such as parseval's identity. the present paper shows a connection between haar wavelets and certain sequences.

Araci et al. introduced a $$p$$ -adic $$(\rho,q)$$ -analogue of the Haar distribution. By means distribution, they constructed -Volkenborn integral. In this paper, by virtue Mahler expansion continuous functions, author gives Radon-Nikodym theorem with respect to -distribution on $$\Bbb Z_p$$ .

In this paper, an efficient numerical scheme based on uniform Haar wavelets is used to solve the non-planar Burgers equation. The quasilinearization technique is used to conveniently handle the nonlinear terms in the non-planar Burgers equation. The basic idea of Haar wavelet collocation method is to convert the partial differential equation into a system of algebraic equations that involves a ...