The Continuous Wavelet Transform and Variable Resolution Time-Frequency Analysis

Abstract

this article, we derived analytic expressions relating the scale at which features occur in the continuous wavelet transform to the associated, time-localized frequency and the frequency parameter of the Morlet wavelet. We also derived an analytic expression for the spread in scale and, hence, frequency in the transform as a function of the bandwidth parameter. Thus, one can derive quantitative information about temporal-- local behavior of the signal from features in the surface and, in an iterative process, refine the mother wavelet to present the features of interest optimally. REFERENCES