Scaling Theorems for Zero Crossings
IEEE Transactions on Pattern Analysis and Machine Intelligence
Scale-Space for Discrete Signals
IEEE Transactions on Pattern Analysis and Machine Intelligence
Ten lectures on wavelets
Scale-Space Derived From B-Splines
IEEE Transactions on Pattern Analysis and Machine Intelligence
The L/sub 2/-Polynomial Spline Pyramid
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiscale curvature-based shape representation using B-spline wavelets
IEEE Transactions on Image Processing
Image representations using multiscale differential operators
IEEE Transactions on Image Processing
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Zero crossings or extrema of a wavelet transform constitute important signatures for signal analysis with the advantage of great simplicity. In this paper, we introduce a fast frequency-estimation method based on zero-crossing counting in the transform domain of a family of differential spline wavelets. The resolution and order of the vanishing moments of the chosen wavelets have a close relation with the frequency components of a signal. Theoretical results on estimating the highest and the lowest frequency components are derived, which are particularly useful for frequency estimation of harmonic signals. The results are illustrated with the help of several numerical examples. Finally, we discuss the connection of this approach with other frequency estimation methods, with the high-order level-crossing analysis in statistics, and with the scaling theorem in computer vision.