The order of a wavelet transform is typically given by the number of vanishing moments of the analysis wavelet. The Strang-Fix conditions imply that the error for an orthogonal wavelet approximation at scale a i = − 2 globally decays as a , where L is the order of the transform. This is why, for a given number of scales, higher order wavelet transforms usually result in better signal approximat...

A new wavelet-based method is presented in this work for estimating and tracking the pitch period. The main idea of the proposed new approach consists in extracting the cepstrum excitation signal and applying on it a wavelet transform whose resulting approximation coefficients are smoothed, for a better pitch determination. Although the principle of the algorithms proposed has already been cons...

We extend our previous work on space-frequency quantization (SFQ) for image coding from wavelet transforms to the more general wavelet packet transforms [2]. The resulting wavelet packet coder offers a universal transform coding framework within the constraints of filterbank structures by allowing joint transform and quantizer design without assuming a priori statistics of the input image. In o...

Asymptotic expansions of the wavelet transform for large and small values of the translation parameter b are obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has al...

We extend our previous work on space-frequency quantization (SFQ) for image coding from wavelet transforms to the more general wavelet packet transforms. The resulting wavelet packet coder offers a universal transform coding framework within the constraints of filterbank structures by allowing joint transform and quantizer design without assuming a priori statistics of the input image. In other...

Wavelet transforms for discrete-time periodic signals are developed. In this nite-dimensional context, key ideas from the continuous-time papers of Daubechies and of Cohen, Daubechies, and Feauveau are isolated to give a concise, rigorous derivation of the discrete-time periodic analogs of orthonormal and symmetric biorthogonal bases of compactly supported wavelets. These discrete-time periodic...

We consider the wavelet transform of a finite, rooted, node-ranked, p-way tree, focusing on the case of binary (p = 2) trees. We study a Haar wavelet transform on this tree. Wavelet transforms allow for multiresolution analysis through translation and dilation of a wavelet function. We explore how this works in our tree context.

Wavelet transforms have become increasingly important in image compression since wavelets allow both time and frequency analysis simultaneously. This paper investigates the fundamental concept behind the wavelet transform and provides an overview of some improved algorithms on the wavelet transform. The latter part of this paper emphasize on lifting scheme which is an improved technique based o...

Welcome to this introductory tutorial on wavelet transforms. The wavelet transform is a relatively new concept (about 10 years old), but yet there are quite a few articles and books written on them. However, most of these books and articles are written by math people, for the other math people; still most of the math people don't know what the other math people are talking about (a math profess...

In the context of image coding, a number of reversible integer-to-integer wavelet transforms are compared on the basis of their lossy compression performance, lossless compression performance, and computational complexity. Of the transforms considered, several were found to perform particularly well, with the best choice for a given application depending on the relative importance of the preced...