Optimization-based quasi-uniform spherical t-design and generalized multitaper for complex physiological time series

07/31/2019

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by   Matt Sourisseau, et al.

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Motivated by the demand to analyze complex physiological time series, we provide a quasi-uniform spherical t-design for any dimensional sphere based on an optimization approach. The design is generalized to achieve a quasi-uniform spherical (k,l)-design for complex sphere of arbitrary dimension. The real and complex designs are applied to construct a generalized multitaper scheme for the nonlinear-type time-frequency analysis, particularly the concentration of frequency and time (ConceFT), which we coin the QU-ConceFT. The proposed QU-ConceFT is applied to visualize the spindle structure in the electroencephalogram signal during the N2 sleep stage.