Abstract-The ridges obtained from chaotic signals can give the relevant information about the phase structures of the dynamical systems. Therefore, a new wavelet ridge determination method for the noisy signals and nonstationary signals, which is based on the singular value decomposition (SVD) has been proposed in this paper. The proposed method has been compared with Carmona method for monocomponent signals, and multicomponent signals. The proposed method is computationally more effective than the Carmona method to determine the actual ridges. Also, the ridges of the periodic limit cycles and chaotic attractors have been determined by using the SVD-based method to find the degree of chaoticity.Index Terms-Instantaneous frequency, singular value decomposition (SVD), wavelet ridge.

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Electrocardiography (ECG) signal is a bioelectrical signal which depicts the cardiac activity of the heart. It is a technique used primarily as a diagnostic tool for various cardiac diseases. ECG provides necessary information on the electrophysiology and changes that may occur in the heart. Due to the increase in mortality rate associated with cardiac diseases worldwide despite recent technological advancement, early detection of these diseases is of paramount importance. This paper has proposed a robust ECG feature extraction technique suitable for mobile devices by extracting only 200 samples between R-R intervals as equivalent R-T interval using Pan Tompkins algorithm at preprocessing stage. The discrete wavelet transform (DWT) of R-T interval samples are calculated and the statistical parameters of wavelet coefficients such as mean, median, standard deviation, maximum, minimum, energy and entropy are used as a time-frequency domain feature. The proposed hybrid technique has been tested by classifying three ECG beats as normal, right bundle branch block (Rbbb) and paced beat using the signals from Massachusetts Institute of Technology Beth Israel Hospital (MIT-BIH) arrhythmia database and processed using Matlab 2013 environment. Classification has been performed using neural network backpropagation algorithm because of its simplicity. While equivalent R-T interval features gives average accuracy of 98.22%, the proposed hybrid method gives a promising result with average accuracy of 99.84% with reduced classifier computational complexity.

A wavelet network circuit implementation for Mexican Hat mother wavelet has been proposed for nonlinear function approximation which can also be used for the realization of the algebraic nonlinear components. The Mexican Hat mother wavelet function has been implemented with discrete circuit components and it has been observed that the experimental waveform obtained from the realized circuit is approximately same as the Spice simulation of the original function. The circuit simulations of exemplar functions implemented in Spice are also given.