A procedure for singularity measurement using wavelet

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.