Fast frequency estimation using spline wavelets

Abstract

An approach for fast frequency estimation using spline wavelet is introduced in this paper, which simply makes use of the zero-crossings of the spline wavelet transforms of a signal. We show that the scale and order of the wavelets have a close relation with the frequency components of the signal. For a random signal with zero means, the lowest frequency component can be obtained by counting the number of zero-crossings of its spline wavelet transforms at sufficiently large scales, while the highest frequency component can be estimated by increasing the order of vanishing moments. A number of numerical examples will be demonstrated. The fast frequency estimation can find many applications such as the search of periodicity and white noise testing. Finally, we show the intrinsic connection of this approach with the level-crossing analysis in statistics and the scaling theorem in computer vision.

Propagation of Random Errors by the Discrete Wavelet Transform Algorithm

“…Many different kinds of wavelets are described in publications, depending on their specificity and properties, they are used to analyze and process measuring signals. The paper presents the wavelets of the "Daubechies" family ("db") [12] and their derivatives "Symlet" ("sym") (used, among others, for image and sound analysis [13]) as well as wavelets of the "Spline" family [14] (used, among others, for the analysis of the condition of machine mechanical elements [15]). In addition, a concept using double-density decomposition ("dden") [16] will be analyzed.…”