Design and Evaluation of Optimal Orthogonal Wavelet With the Least Length of Wavelet Filters Using Spectral Matching

This paper presents a method to find a matched wavelet with the least length of wavelet filters using spectral matching. The existing problem in algorithm of designing in spectral fashion is described, and the corresponding solution is provided. The problem encountered in the common algorithm is the heavy computations in spectral phase matching that often produces errors in machine running, and consequently, the phase matching algorithm becomes incomplete. In this paper, the computational costs and errors arising from such phase matching are improved. Then, a method is proposed, thereby enabling the construction of orthogonal wavelet transform filters with minimum length. The proposed approach is examined with a signal from the real world. The compression of neural signals in implantable microsystems is provided, and its performance is compared with the superior wavelets. It yields higher compression rate than other well-reported wavelets, such as sym4, db4, and sym7, as well as the designed wavelet is able to perform more efficient than general wavelets in noisy conditions. These appropriate results are obtained because of designing matched wavelet with the least length of filters.