A procedure for singularity measurement using wavelet
Nugraha H.B.a, Langi A.Z.R.a
a Department of Electrical Engineering, IURC Microelectronics, Bandung Institute of Technology, West Java, 40132, Indonesia
Abstract
© 2002 IEEE.Two important key factors in signal processing are singularity analysis and dynamical behaviour, as singularities and dynamics carry most of the signal information. Wavelet analysis is very good in localization of singularities. This paper describes a method in measuring singularity of a simple well-known one-dimensional signal using a wavelet approach. The singularity, by mean of a Lipschitz exponent of a function, is measured by taking the slope of a log-log plot of scales and wavelet coefficients along modulus maxima lines of a wavelet transform. Using this method, we measure the dimension of a particular function f(t)=1-|c-t|λ where c is a constant and λ varies from 0.1 to 0.9 with a 0.1 interval. This procedure yields good estimation of the Lipschitz exponent when 0.5≤λ≤0.9.
Author keywords
A-wavelet transform,Continuous Wavelet Transform,Dynamical behaviours,Lipschitz exponents,One dimensional signal,Singularity analysis,Time frequency analysis,Wavelet coefficients
Indexed keywords
Chaos,Continuous wavelet transforms,Fourier transforms,Fractals,Microelectronics,Signal analysis,Signal processing,Time frequency analysis,Wavelet analysis,Wavelet transforms