Fast frequency estimation using spline wavelets
Yu‐Ping Wang · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2005
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.