Singularity and Similarity Detection from Signals Using Wavelet Transform

TL;DR

This paper introduces wavelet-based methods for detecting singularities and estimating self-similarity in signals, enhancing analysis of fractal and self-affine data.

Contribution

It presents a normalized wavelet scalogram for singularity detection and applies wavelet auto-covariance to estimate self-similarity exponents.

Findings

Effective detection of jumps and cusps in signals

Accurate estimation of self-similarity exponents

Enhanced analysis of fractal signals

Abstract

The wavelet transform and related techniques are used to analyze singular and fractal signals. The normalized wavelet scalogram is introduced to detect singularities including jumps, cusps and other sharply changing points. The wavelet auto-covariance is applied to estimate the self-similarity exponent for statistical self-affine signals.