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Discrete wavelet transforms in VLSI

[1992] Proceedings of the International Conference on Application Specific Array Processors, 2003
Three architectures, based on linear systolic arrays, for computing the discrete wavelet transform, are described. The AT/sup 2/ lower bound for computing the DWT in a systolic model is derived and shown to be AT/sup 2/= Omega (N/sup 2/N/sub w/k). Two of the architectures are within a factor of log N from optimal, but they are of practical importance ...
M. Vishwanath   +2 more
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On the discrete wavelet transform and shiftability

Proceedings of 27th Asilomar Conference on Signals, Systems and Computers, 2002
We analyze the relationship between the change that is observed in the wavelet coefficients when a signal is time shifted and the time and frequency distributions of the wavelet functions. We address the effects of shift variance and show how it can be useful. >
Feng Bao, Nurgun Erdol
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VLSI implementation of discrete wavelet transform

IEEE Transactions on Very Large Scale Integration (VLSI) Systems, 1996
This paper presents a VLSI implementation of discrete wavelet transform (DWT). The architecture is systolic in nature and performs both high-pass and low-pass coefficient calculations with only one set of multipliers, in contrast to the approaches presented in the literature. The architecture is simple, modular, and cascadable, and has been implemented
Sethuraman Panchanathan   +2 more
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The Discrete Wavelet Transform

2004
The MRA structure allows for the convenient, fast, and exact calculation of the wavelet coefficients of an L 2 function by providing a recursion relation between the scaling coefficients at a given scale and the scaling and wavelet coefficients at the next coarser scale. In order to specify this relation, let {V j × be an MRA with scaling function φ(x).
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Initialization of orthogonal discrete wavelet transforms

IEEE Transactions on Signal Processing, 2000
Summary: The symptotic formulae of both the approximation error and the systematic error of a special prefilter projection and the quantitative estimates of the upper bounds of the errors are obtained. In addition, it is shown that for the Daubechies' orthogonal wavelet basis, the estimated constant is optimal.
Zheng Bao, Jiancheng Zhang
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The Discrete Wavelet Transform in Practice

2000
In this chapter we present the finite discrete wavelet transform (DWT) using matrices. The main difference between the description of the DWT in this chapter, compared to the description given in the previous chapter, is now we consider the DWT for discrete data, as opposed to continuous functions. We first provide a brief introduction to matrix theory
Mallet, Y., De Vel, O., Coomans, D.
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VLSI architectures for the discrete wavelet transform

IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, 1995
Summary: A class of VLSI architectures based on linear systolic arrays, for computing the 1-D discrete wavelet transform (DWT), is presented. The various architectures of this class differ only in the design of their routing networks, which could be systolic, semisystolic, or RAM-based. These architectures compute the recursive pyramid algorithm, which
Mary Jane Irwin   +2 more
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CONVOLUTION FOR THE DISCRETE WAVELET TRANSFORM

International Journal of Wavelets, Multiresolution and Information Processing, 2011
Translation and convolution associated with the discrete wavelet transform are investigated using properties of Calderón–Zygmund operator and Riesz fractional integral operator. Dual convolution is also studied. The wavelet convolution is applied to approximate functions belonging to certain Lp-spaces.
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Discrete Wavelet Transform Signal Analyzer

IEEE Transactions on Instrumentation and Measurement, 2007
This paper addresses the problem of processing biological data, such as cardiac beats in the audio and ultrasonic range, and on calculating wavelet coefficients in real time, with the processor clock running at a frequency of present application-specified integrated circuits and field programmable gate array.
Cox, Pedro Henrique   +1 more
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Numerical Condition of Discrete Wavelet Transforms

SIAM Journal on Matrix Analysis and Applications, 1997
In many applications biorthogonal wavelets have been used rather than orthogonal ones, since the latter might exclude other useful properties like symmetry in the case of compactly supported wavelets. Thus one would like to study stability of biorthogonal wavelets and obtain quantitative information about sensitivity to noise in the data or ...
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