fda (version 6.2.0)

fourier: 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)

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 functions.

Arguments

x

a vector of argument values at which the Fourier basis functions are to be evaluated.

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.

References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

See Also

fourierpen

Examples

#  set up a set of 11 argument values
x <- seq(0,1,0.1)
names(x) <- paste("x", 0:10, sep="")
#  compute values for five Fourier basis functions
#  with the default period (1) and derivative (0)
(basismat <- fourier(x, 5))

# Create a false Fourier basis, i.e., nbasis = 1
# = a constant function
fourier(x, 1)