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

Motivated by the demand to analyze complex time series, we provide a quasi-uniform spherical $(k,l)$-design for any dimensional {\em complex} sphere based on an optimization approach. We provide the first theoretical justification of the existence of the optimal spherical $(k,l)$-design with the optimal order for any dimensional complex sphere. The design is also applicable to achieve a quasi-uniform spherical $t$-design for real 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.

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