A NEW DISCRETE WAVELET TRANSFORM
Alexandru Isar, Dorina Isar · 2002
The Discrete Wavelet Transform (DWT) has two parameters: the mother of wavelets and the number of iterations. Selecting different parameters for different DWT of the same signal, different energy concentrations in the wavelet domain are obtained. So, for a particular signal there is a better pair of parameters that realizes the best energy concentration in the wavelet transform domain. In applications is difficult to find this best pair of parameters. This is the reason why the aim of this paper is to introduce a new DWT less sensitive to the parameter selection. This transform is built using a technique very modern in telecommunications, the diversity enhancement. The diversity is enhanced in the wavelet transform domain computing different DWT, of the same signal, with different parameters. So, the input signal, represented by a vector, is transformed into a matrix. Each column of this matrix represents the DWT of the input signal, computed with a different pair of parameters. This matrix represents the result of the new discrete wavelet transform, named the Diversity Enhanced Discrete Wavelet Transform, (DEDWT). The new transform can be used with good results in denoising applications, especially for low SNR signals. The discrete wavelet transform, DWT, realizes a concentration of the energy of the input signal in a small number of coefficients. This concentration's enhancement is useful for the reduction of the number of operations in the application considered. For a given signal, using different wavelet's mothers, different energy concentrations are obtained. So, for a given input signal there is a best wavelet's mother, that realizes the higher energy concentration. The aim of this paper is to propose a new DWT less sensitive to the selection of the wavelet’s mother. The construction is based on the diversity enhancement’s principle. Such a transformation is useful for the denoising of low signal to noise ratio, SNR, signals. In the second section of this paper is presented the construction of the new transform, the DEDWT. The computation of its inverse is also described. The central result of this paper, described in the third section, is the application of the new transformation in denoising applications. In the forth section some simulation results are presented. The last section is dedicated to conclusions.