Fourier Basis Function Values
Fourier Basis Function Values
DESCRIPTION:
Evaluates a set of Fourier basis functions, or a derivative of these
functions, at a set of arguments.
USAGE:
fourier(x, nbasis=n, period=span, nderiv=0)
REQUIRED ARGUMENTS:
- x
-
A vector of argument values at which the Fourier basis functions are to
evaluated.
OPTIONAL ARGUMENTS:
- nbasis
-
The number of basis functions in the Fourier basis. The first basis
function is the constant function, followed by sets of sine/cosine
pairs. Normally the number of basis functions will be an odd. The
default number is the number of argument values.
- period
-
The width of an interval over which all sine/cosine basis functions
repeat themselves. The default is the difference between the largest
and smallest argument values.
- nderiv
-
The derivative to be evaluated. The derivative must not exceed the
order. The default derivative is 0, meaning that the basis functions
themselves are evaluated.
VALUE:
A matrix of function values. The number of rows equals the number of
arguments, and the number of columns equals the number of basis
EXAMPLES:
# set up a set of 11 argument values
x <- seq(0,1,0.1)
# compute values for five Fourier basis functions
# with the default period (1) and derivative (0)
basismat <- fourier(x, 5)