dpss

Utility functions for calculating multitaper measurements (MTM). Mainly contains functions for calculating Discrete Prolate Spheroidal Sequences (DPSS)

copyright

adjTomo Dev Team (adjtomo@gmail.com), 2022 Lion Krischer (krischer@geophysik.uni-muenchen.de), 2016 Martin Luessi (mluessi@nmr.mgh.harvard.edu), 2012

License : BSD 3-clause

Module Contents

Functions

tridisolve(d, e, b[, overwrite_b])

Symmetric tridiagonal system solver, from Golub and Van Loan pg 157

tridi_inverse_iteration(d, e, w[, x0, rtol])

Perform an inverse iteration to find the eigenvector corresponding

sum_squared(x)

Compute norm of an array

dpss_windows(n, half_nbw, k_max[, low_bias, ...])

Returns the Discrete Prolate Spheroidal Sequences of orders [0,Kmax-1]
dpss.tridisolve(d, e, b, overwrite_b=True)[source]

Symmetric tridiagonal system solver, from Golub and Van Loan pg 157

Note

Copied from the mne-python package so credit goes to them. https://github.com/mne-tools/mne-python/blob/master/mne/time_frequency/ multitaper.py

Parameters

  • d (ndarray) – main diagonal stored in d[:]

  • e (ndarray) – superdiagonal stored in e[:-1]

  • b (ndarray) – RHS vector

:rtype x : ndarray :return: Solution to Ax = b (if overwrite_b is False). Otherwise solution is

stored in previous RHS vector b

dpss.tridi_inverse_iteration(d, e, w, x0=None, rtol=1e-08)[source]

Perform an inverse iteration to find the eigenvector corresponding to the given eigenvalue in a symmetric tridiagonal system.

Note

Copied from the mne-python package so credit goes to them. https://github.com/mne-tools/mne-python/blob/master/mne/time_frequency/ multitaper.py

Parameters

  • d (ndarray) – main diagonal stored in d[:]

  • e (ndarray) – off diagonal stored in e[:-1]

  • w (float) – eigenvalue of the eigenvector

  • x0 (ndarray) – initial point to start the iteration

:type rtol : float :param rtol: tolerance for the norm of the difference of iterates :rtype: ndarray :return: The converged eigenvector

dpss.sum_squared(x)[source]

Compute norm of an array

Parameters

x (array) – Data whose norm must be found

Return type

float

Returns

Sum of squares of the input array X

dpss.dpss_windows(n, half_nbw, k_max, low_bias=True, interp_from=None, interp_kind='linear')[source]

Returns the Discrete Prolate Spheroidal Sequences of orders [0,Kmax-1] for a given frequency-spacing multiple NW and sequence length N. Rayleigh bin parameter typical values of half_nbw/nw are 2.5,3,3.5,4.

Note

Tridiagonal form of DPSS calculation from:

Slepian, D. Prolate spheroidal wave functions, Fourier analysis, and uncertainty V: The discrete case. Bell System Technical Journal, Volume 57 (1978), 1371430

Note

This function was copied from NiTime

Parameters

  • n (int) – Sequence length

  • half_nbw (float) – unitless standardized half bandwidth corresponding to 2 * half_bw = BW*f0 = BW*N/dt but with dt taken as 1

  • k_max (int) – Number of DPSS windows to return is Kmax (orders 0 through Kmax-1)

  • low_bias (Bool) – Keep only tapers with eigenvalues > 0.9

  • interp_from (int (optional)) – The dpss can be calculated using interpolation from a set of dpss with the same NW and Kmax, but shorter N. This is the length of this shorter set of dpss windows.

  • interp_kind (str (optional)) – This input variable is passed to scipy.interpolate.interp1d and specifies the kind of interpolation as a string (‘linear’, ‘nearest’, ‘zero’, ‘slinear’, ‘quadratic, ‘cubic’) or as an integer specifying the order of the spline interpolator to use.

Return type

tuple

Returns

(v, e), v is an array of DPSS windows shaped (Kmax, N), e are the eigenvalues