Relation between Spectrum Density and Wavelet Transform of Correlation Function

Abstract

This paper concerns properties of wavelet transform of a correlation function from the viewpoint of spectrum analysis. First of all, a basic characteristic is derived as a relation between the wavelet transform and the spectrum density. The relation shows that the wavelet transform can be treated as an estimate of the corresponding spectrum density if an analyzing wavelet is chosen appropriately. Its bias from the true value is also obtained for this case. Moreover, a selection of an analyzing wavelet is considerd to reduce the bias. This consideration provides validity of using the Gabor function as an analyzing wavelet for applications of wavelet transform of a correlation function.