The popular approach to phase and amplitude estimation is to exploit the analytic signal approach based on the Hilbert Transform (HT) or, equivalently, the wavelet transform with a complex wavelet 1, 13, 14, 15. One of the directions in this development is to adjust stimulation parameters according to a peripheral or neurophysiological signal’s phase and amplitude computed on the fly 6, 7, 8, 9, 10, 11, 12. A special application is developing efficient sensing algorithms for adaptive deep brain stimulation, a recent advancement of a widely used treatment option for Parkinson’s disease and other neurological disorders 5. Estimation of the instantaneous phase and amplitude is essential for electrical and mechanical engineering, synchronization studies of oscillatory systems of different nature, time series analysis of physiological data, and, in particular, for neuroscience 1, 2, 3, 4.
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