Convert Functional Data to Basis Coefficients

Project functional data onto a basis system and return coefficients. Supports B-spline and Fourier basis. Works with both regular fdata and irregular irregFdata objects.

Usage

fdata2basis(x, nbasis = 10, type = c("bspline", "fourier"), ...)

# S3 method for class 'fdata'
fdata2basis(x, nbasis = 10, type = c("bspline", "fourier"), ...)

# S3 method for class 'irregFdata'
fdata2basis(x, nbasis = 10, type = c("bspline", "fourier"), ...)

Arguments

x

An object of class 'fdata' or 'irregFdata'.

nbasis

Number of basis functions (default 10).

type

Type of basis: "bspline" (default) or "fourier".

...

Additional arguments (currently unused).

Value

A matrix of coefficients (n x nbasis).

Details

For regular fdata objects, all curves are projected onto the same basis evaluated at the common grid points.

For irregular irregFdata objects, each curve is individually fitted to the basis using least squares at its own observation points. This is the preferred approach for sparse/irregularly sampled data as it avoids interpolation artifacts.

Examples

# Regular fdata
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 20, 50)
for (i in 1:20) X[i, ] <- sin(2*pi*t) + rnorm(50, sd = 0.1)
fd <- fdata(X, argvals = t)
coefs <- fdata2basis(fd, nbasis = 10, type = "bspline")

# Irregular fdata (sparsified)
ifd <- sparsify(fd, minObs = 10, maxObs = 20, seed = 42)
coefs_irreg <- fdata2basis(ifd, nbasis = 10, type = "bspline")