Genesis of the Solitary Wavelet
Sai Venkatesh Balasubramanian · viXra · 2015
A solitary wavelet, based on the hyperbolic secant function is proposed, characterized and applied to real-time data. Numerical analysis of the solitary wavelet reveals that it has a huge number of vanishing higher order moments, tending rapidly towards zero with a negative logarithmic slope. It is seen that the wavelet has a very low number of oscillatory sub-lobes, thus making it the ideal candidate to perform signal analysis of burst-type phenomena without undergoing multiple levels of filtering and approximation, and this concept is illustrated by effectively detecting the QRS complex of an ECG cycle without undergoing multiple filtering levels. The ability of the proposed wavelet to perform analysis of a diverse variety of real time data without multiple levels of decomposition and reconstruction forms the novelty of the present work.