Analysis of the fetal heart rate during pregnancy is essential for monitoring the proper development of the fetus. Current fetal heart monitoring techniques lack the accuracy in fetal heart rate monitoring and features acquisition, resulting in diagnostic medical issues. The challenge lies in the extraction of the fetal ECG from the mother ECG during pregnancy. This approach has the advantage of being a reliable and non-invasive technique. In the present paper, a wavelet/multiwavelet method is proposed to perfectly extract the fetal ECG parameters from the abdominal mother ECG. In a first step, due to the wavelet/mutiwavelet processing, a denoising procedure is applied to separate the noised parts from the denoised ones. The denoised signal is assumed to be a mixture of both the MECG and the FECG. One of the well-known measures of accuracy in information processing is the concept of entropy. In the present work, a wavelet/multiwavelet Shannon-type entropy is constructed and applied to evaluate the order/disorder of the extracted FECG signal. The experimental results apply to a recent class of Clifford wavelets constructed in Arfaoui, et al. J. Math. Imaging Vis. 2020, 62, 73–97, and Arfaoui, et al. Acta Appl. Math. 2020, 170, 1–35. Additionally, classical Haar–Faber–Schauder wavelets are applied for the purpose of comparison. Two main well-known databases have been applied, the DAISY database and the CinC Challenge 2013 database. The achieved accuracy over the test databases resulted in Se = 100%, PPV = 100% for FECG extraction and peak detection.

In the present work, magnesium oxide (MgO) and lead oxide (PbO) nanoparticles were prepared by the co-precipitation method. Their structural parameters and morphology were investigated using XRD, HRTEM, and FTIR. The formation of the phases was seen to have small average crystallite sizes and an orthorhombic crystal structure for both MgO and PbO nanoparticles. The results of HR-TEM showed irregularly shaped nanoparticles: quasi-spherical or rod-like shapes and spherical-like shapes for MgO and PbO nanoparticles, respectively. The produced nanoparticles’ size using X-ray diffraction analysis was found to be 17 nm and 41 nm for MgO and PbO nanoparticles, respectively. On the other hand, it was observed from the calculations that the optical band gap obeys an indirect allowed transition. The calculated values of the band gap were 4.52 and 4.28 eV for MgO and PbO NPs, respectively. The MB was extracted from the wastewater using the prepared composites via absorption. Using a variety of kinetic models, the adsorptions were examined. Out of all the particles, it was discovered that the composites were best. Furthermore, of the models currently under consideration, the pseudo-second-order model best fit the degradation mechanism. The resultant composites could be beneficial for degrading specific organic dyes for water purification, as well as applications needing a wider optical band gap.