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Modular wavelet transform in the neural


N. I. Chervyakov, P. A. Lyakhov

Currently, wavelets are widely used for pattern recognition, speech processing, image compression, denoising signals and many others. This article examines the use of residue number system to implement the wavelet transform, and, in particular, the proposed implementation of the wavelet filters using finite ring neural networks. There are two main advantages of modular arithmetic: 1. Arithmetic operations of addition, subtraction and multiplication are performed without division, in contrast to the positional representation of numbers. 2. For each of the values of the moduli residue number system, arithmetic operations are performed with a pair of corresponding residues in parallel. In the article the basic principles for the implementation of modular adders and multipliers are shown. Advantages and disadvantages of each of the above methods are given. The possibility of realization of operations carried out in residue number system using finite ring neural networks. The use of such neural networks can improve system performance such as performance and fault tolerance. All the above is applied in order to show the way to implement a discrete wavelet transform, as defined in the residue number system, using finite ring neural networks.

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