Computes the inverse Fourier transform of a B-spline basis function of degree k,
indexed by i, using its truncated power expansion representation. This is used
to construct spectral representations of B-spline basis functions.
Usage
inverse_fourier_truncated_power(knots, i, k, tau)
Arguments
- knots
A numeric vector of knots.
- i
An integer index indicating the position in the knot sequence for which to compute the coefficients.
- k
The degree of the B-spline basis function (must be 0, 1, or 2).
- tau
A numeric vector of frequencies at which to evaluate the inverse Fourier transform.
Value
A complex-valued vector of the same length as tau, giving the inverse Fourier transform
of the basis function evaluated at each frequency.
Examples
knots <- c(0, 1, 2, 3, 4, 5)
tau <- seq(-5, 5, length.out = 200)
rho <- inverse_fourier_truncated_power(knots, i = 1, k = 1, tau = tau)
plot(tau, Re(rho), type = "l", main = "Real part of Fourier transform")
