scholarly journals VLSI Architectures for the 4-Tap and 6-Tap 2-D Daubechies Wavelet Filters Using Algebraic Integers

2013 ◽  
Vol 60 (6) ◽  
pp. 1455-1468 ◽  
Author(s):  
Shiva Kumar Madishetty ◽  
Arjuna Madanayake ◽  
Renato J. Cintra ◽  
Vassil S. Dimitrov ◽  
Dale H. Mugler
Keyword(s):  
Daubechies Wavelet ◽  
Algebraic Integers ◽  
Wavelet Filters ◽  
Vlsi Architectures

VLSI ARCHITECTURES OF DAUBECHIES WAVELET TRANSFORMS USING ALGEBRAIC INTEGERS

2004 ◽  
Vol 13 (06) ◽  
pp. 1251-1270 ◽  
Author(s):  
KHAN WAHID ◽  
VASSIL DIMITROV ◽  
GRAHAM JULLIEN
Keyword(s):  
Power Dissipation ◽  
Wavelet Transforms ◽  
Algebraic Integer ◽  
Vlsi Architecture ◽  
Systolic Arrays ◽  
Discrete Wavelet ◽  
Daubechies Wavelet ◽  
Vlsi Architectures ◽  
Data Bus ◽  
Zero Tree

Two-Dimensional Wavelet Transforms have proven to be highly effective tools for image analysis. In this paper, we present a VLSI implementation of four- and six-coefficient Daubechies Wavelet Transforms using an algebraic integer encoding representation for the coefficients. The Daubechies filters (DAUB4 and DAUB6) provide excellent spatial and spectral locality, properties which make it useful in image compression. In our algorithm, the algebraic integer representation of the wavelet coefficients provides error-free calculations until the final reconstruction step. This also makes the VLSI architecture simple, multiplication-free and inherently parallel. Compared to other DWT algorithms found in the literature, such as embedded zero-tree, recursive or semi-recursive, linear systolic arrays and conventional fixed-point binary architectures, it has reduced hardware cost, lower power dissipation and optimized data-bus utilization. The architecture is also cascadable for computation of one- or multi-dimensional Daubechies Discrete Wavelet Transforms.

Pseudo-Anosov Theory

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Braid Groups ◽  
Intersection Numbers ◽  
Branched Covers ◽  
Algebraic Integers ◽  
Dehn Twists ◽  
Mapping Classes ◽  
Dynamical Properties

This chapter focuses on the construction as well as the algebraic and dynamical properties of pseudo-Anosov homeomorphisms. It first presents five different constructions of pseudo-Anosov mapping classes: branched covers, constructions via Dehn twists, homological criterion, Kra's construction, and a construction for braid groups. It then proves a few fundamental facts concerning stretch factors of pseudo-Anosov homeomorphisms, focusing on the theorem that pseudo-Anosov stretch factors are algebraic integers. It also considers the spectrum of pseudo-Anosov stretch factors, along with the special properties of those measured foliations that are the stable (or unstable) foliations of some pseudo-Anosov homeomorphism. Finally, it describes the orbits of a pseudo-Anosov homeomorphism as well as lengths of curves and intersection numbers under iteration.

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