New Type of Gegenbauer–Hermite Monogenic Polynomials and Associated Clifford Wavelets

Abstract

In the present work, new classes of wavelet functions are presented in the framework of Clifford analysis. Firstly, some classes of new monogenic polynomials are provided based on 2-parameters weight functions. Such classes englobe the well known Jacobi, Gegenbauer ones. The discovered polynomial sets are next applied to introduce new wavelet functions. Reconstruction formula as well as Fourier-Plancherel rules have been proved.

Towards New Multiwavelets: Associated Filters and Algorithms. Part I: Theoretical Framework and Investigation of Biomedical Signals, ECG and Coronavirus Cases

“…The regions of anomalies, and communication constitute some type of helices which correspond to the singular, and optimum points in the numerical series issued from the biological ones. See [7,24,31,72] for more details.…”

“…Next, as it is now well known that wavelets, and multi-wavelets are powerful tools to detect the transmembrane segments in proteins' series ( [7,13,14,31,72]), and in order to prove the applicability, and thus the useful aspect of our multi-wavelet we proposed to focus on the possible detection, and/or prediction of alphahelices in the considered protein. We subsequently propose to predict the locations of these regions by statistical processing applying the HSch multi-wavelet.…”

“…One of our aims in the present work is to improve multi-wavelet notion by adopting more general families of explicit multiwavelets constructed using independent components for multidimensional scaling functions. Readers may also consult [12,7,8,[33][34][35][36]72] for more applications of the concepts of wavelets, and multi-wavelets, especially, on bio-signals.…”

“…However, we recall that other examples of multi-wavelets may be also obtained even explicitly by applying other scaling functions, and/or wavelet mothers different from the present case. Some interesting cases may be found in [7,8]. See also [17, 30,32,39, 45, 51, 53-55, 61, 64, 66-68] for more methods, and applications.…”

A Wavelet-Based Method for the Impact of Social Media on the Economic Situation: The Saudi Arabia 2030-Vision Case

“…Fischer et al in [12] applied a wavelet denoising method to predict transmembrane proteins helices. Arfaoui et al [13,14], Bin et al [15,16] and Cattani et al [17][18][19][20][21] conducted wavelet methods for the modeling, forecasting, complexity and symmetries in proteins and DNA series. Schleicher [22] conducted a fascinating study on the use of wavelet methods in econo-financial fields, such as filtering, thresholding, denoising, forecasting, etc.…”