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Detecting highly oscillatory signals by chirplet path pursuit. (English) Zbl 1144.94003
The paper deals with the problem of detecting one-dimensional highly oscillatory signals, named chirps, from very noisy measurements. The proposed detection strategy exploits a family of multiscale chirplets, i.e. templates which provide good local approximations of chirps, and uses a chirplet graph to chain chirplets together adaptively as to form a signal which is physically meaningful, and whose correlation with the data is largest. This is achieved by finding the best path in the chirplet graph which maximizes a test statistic based on the weighted sum of squares of the empirical correlation coefficients, and can be accomplished by dynamic programming method; particularly using ChirpLab - the developed and publicly available Matlab software package. To demonstrate the performance of the method, extensive simulation study is provided. The numerical experiments show that the approach ensures high flexibility and adaptivity to the unknown structures of broad classes of nonstationary signals.
MSC:
94A13Detection theory
65T99Numerical methods in Fourier analysis
42C15General harmonic expansions, frames
Software:
Matlab