Abstract
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.
Highlights
Zero crossings or extrema of a signal constitute very important features that have been used in signal processing applications for detection of weak signals, search for periodicity, white-noise testing, and so on, because of their great simplicity [1]
The higher-order zero crossings were utilized for fast detection of contractions in uterine electromyography [2] and for discrimination of discontinuous breath sounds [3]
Even though zero crossings have been used in the wavelet domain for signal reconstruction, it remains unclear how they are related to the spectrum of a signal
Summary
Zero crossings or extrema of a signal constitute very important features that have been used in signal processing applications for detection of weak signals, search for periodicity, white-noise testing, and so on, because of their great simplicity [1]. The illustrations of these theoretical results will be presented with the help of several numerical examples. We conclude the paper with a discussion on the connection of the proposed method with other frequency estimation approaches, with high-order level-crossing analysis in statistics, and with the scaling theorem in computer vision
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