tedana.utils.create_legendre_polynomial_basis_set

create_legendre_polynomial_basis_set(n_vols: int, dtrank: int | None = None) → ndarray[tuple[int, ...], dtype[_ScalarType_co]][source]

Create Legendre polynomial basis set for detrending time series.

Parameters:

  • n_vols (int) – The number of time points in the fMRI time series

  • dtrank (int, optional) – Specifies degree of Legendre polynomial basis function for estimating spatial global signal. Default: None If None, then this is set to 1+floor(n_vols/150)

Returns:

legendre_arr ((T X R) np.ndarray) – A time by rank matrix of the first dtrank order Legendre polynomials. These include: Order 0: y = 1 Order 1: y = x Order 2: y = 0.5*(3*x^2 - 1) Order 3: y = 0.5*(5*x^3 - 3*x) Order 4: y = 0.125*(35*x^4 - 30*x^2 + 3) Order 5: y = 0.125*(63*x^5 - 70*x^3 + 15x)