Slepian sequences (DPSS)

The discrete prolate spheroidal sequences (DPSS), or Slepian sequences, are the family of tapers that solve a precise optimization: for a chosen time-bandwidth product they maximally concentrate spectral energy within a band of half-width W around each frequency while minimizing leakage outside it. They are indexed by an integer order, and the first few (those with eigenvalues near one) are almost perfectly concentrated.

The key design parameter is the time-bandwidth product NW (the product of record length and half-bandwidth). It sets the spectral resolution 2W and the number of well-concentrated tapers, roughly 2NW minus 1. These orthogonal tapers are the ingredients of Thomson's multitaper method: each provides a nearly independent look at the same band, and averaging their eigenspectra reduces variance without the segment-splitting of Welch's method.