3.4 Multiresolution Signal Analysis with Haar Bases An important and attractive feature of the Haar basis is that it provides a multiresolution analysis of a signal.

When J = 0 we refer to this system simply as the Haar wavelet system on [0, 1]. Here, the choice of k’s and the assumption about J ≥ 0 are necessary so that the system we have created is a …

My interest in this topic is in its role in the theory of automorphic forms and representaions. I am currently reading on Bump's Automorphic Forms and Representations, Chapters 2 and 3, which …

The Haar wavelet basis for L2(R) breaks down a signal by looking at the di erence between piecewise constant approximations at dif-ferent scales. It is the simplest example of a wavelet …

The powerful construct of the Haar measure, introduced by Alfred Haar in 1933, shows that many of these groups come with an essentially unique (up to a scalar factor) measure.

Construction of the Brownian motion We will construct the Brownian motion on the interval 0 t 1 { the restriction to a nite interval is a simple convenience but by no means a necessity. The Haar …

The Haar function, being an odd rectangular pulse pair, is the simplest and oldest orthonormal wavelet with compact support. In the meantime, several definitions of the Haar functions and …