fourier_basis_expansion {MECfda} | R Documentation |
Fourier basis expansion for functional variable data
Description
For a function f(x), x\in\Omega
, and a basis function sequence \{\rho_k\}_{k\in\kappa}
,
basis expansion is to compute \int_\Omega f(t)\rho_k(t) dt
.
Here we do basis expansion for all f_i(t), t\in\Omega = [t_0,t_0+T]
in functional variable data, i=1,\dots,n
.
We compute a matrix (b_{ik})_{n\times p}
, where b_{ik} = \int_\Omega f(t)\rho_k(t) dt
.
The basis used here is the Fourier basis,
\frac{1}{2},\ \cos(\frac{2\pi}{T}k[x-t_0]),\ \sin (\frac{2\pi}{T}k[x-t_0])
where x\in[t_0,t_0+T]
and k = 1,\dots,p_f
.
Usage
fourier_basis_expansion(object, order_fourier_basis)
## S4 method for signature 'functional_variable,integer'
fourier_basis_expansion(object, order_fourier_basis)
Arguments
object |
a |
order_fourier_basis |
the order of Fourier basis, |
Value
Returns a numeric matrix, (b_{ik})_{n\times p}
, where b_{ik} = \int_\Omega f(t)\rho_k(t) dt
.
Author(s)
Heyang Ji
[Package MECfda version 0.2.0 Index]