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Some New Continuous Wavelets Based on Laguerre Polynomials Applied in Pattern Detection of Noisy Signals.

Bruno Peachap A, Daniel Tchiotsop

In this work, we propose a new basis of wavelets constructed using Laguerre polynomials. Several methods of wavelet construction like Daubechies, splines and coiflets are present in the literature without an exhaustive approach using orthogonal polynomials, and more precisely the Laguerre polynomials. The generalized Laguerre polynomials under certain conditions oscillate like wavelets, as such; we present a method of continuous (wavelets construction, using the generalized Laguerre polynomials, as well as a proof by mathematical induction that the constructed wavelets respect the admissibility condition of wavelets. The constructed wavelets are further applied in the detection of a pattern in a signal. The results show that, even under the influence of white Gaussian noise, the pattern is accurately detected.