xnn.common.models.pme.bspline_moduli#

xnn.common.models.pme.bspline_moduli(size, order, dtype, device)[source]#

|b(m)|^2 of the Euler exponential spline along one mesh axis (paper eq 4.4).

1 / |b(m)|^2 = | sum_{k=0}^{p-2} M_p(k + 1) exp(2 pi i m k / K) |^2 for the K frequencies m in FFT order. A vanishing denominator (odd orders at the Nyquist frequency) is replaced by the mean of its neighbors, the usual safeguard.

Parameters:
  • size (int) – Mesh points K along the axis.

  • order (int) – Spline order p.

  • dtype (dtype) – Of the returned tensor.

  • device (device) – Of the returned tensor.

Returns:

|b(m)|^2, shape (K,).

Return type:

Tensor