create.fourier.basis: Create a Fourier Basis

Description

Create an Fourier basis object defining a set of Fourier functions with specified period.

Usage

create.fourier.basis(rangeval=c(0, 1), nbasis=3,
              period=diff(rangeval), dropind=NULL, quadvals=NULL,
              values=NULL, basisvalues=NULL, names=NULL,
              axes=NULL)

Arguments

rangeval

a vector of length 2 containing the initial and final values of the interval over which the functional data object can be evaluated.

nbasis

positive odd integer: If an even number is specified, it is rounded up to the nearest odd integer to preserve the pairing of sine and cosine functions. An even number of basis functions only makes sense when there are always only an even

period

the width of any interval over which the Fourier functions repeat themselves or are periodic.

dropind

an optional vector of integers specifiying basis functions to be dropped.

quadvals

an optional matrix with two columns and a number of rows equal to the number of quadrature points for numerical evaluation of the penalty integral. The first column of quadvals contains the quadrature points, and the second co

values

an optional list of matrices with one row for each row of quadvals and one column for each basis function. The elements of the list correspond to the basis functions and their derivatives evaluated at the quadrature points con

basisvalues

an optional list of lists, allocated by code such as vector("list",1). This field is designed to avoid evaluation of a basis system repeatedly at a set of argument values. Each sublist corresponds to a specific set of argument values, and

names

either a character vector of the same length as the number of basis functions or a simple stem used to construct such a vector. If nbasis = 3, names defaults to c('const', 'cos', 'sin'). If nbasis >

axes

an optional list used by selected plot functions to create custom axes. If this axes argument is not NULL, functions plot.basisfd, plot.fd, plot.fdSmooth

`Value`

a basis object with the type fourier.

`Details`

Functional data objects are constructed by specifying a set of basis
  functions and a set of coefficients defining a linear combination of
  these basis functions.  The Fourier basis is a system
  that is usually used for periodic functions.  It has the advantages
  of very fast computation and great flexibility.   If the data are
  considered to be nonperiod, the Fourier basis is usually preferred.
  The first Fourier basis function is the constant function.  The
  remainder are sine and cosine pairs with integer multiples of the
  base period. The number of basis functions generated is always odd.

`See Also`

basisfd,
  create.bspline.basis,
  create.constant.basis,
  create.exponential.basis,
  create.monomial.basis,
  create.polygonal.basis,
  create.polynomial.basis,
  create.power.basis

`Examples`

Run this code# Create a minimal Fourier basis for annual data
#  using 3 basis functions
yearbasis3 <- create.fourier.basis(c(0,365),
                    axes=list("axesIntervals") )
#  plot the basis
plot(yearbasis3)

# Identify the months with letters
plot(yearbasis3, axes=list('axesIntervals', labels=monthLetters))

# The same labels as part of the basis object
yearbasis3. <- create.fourier.basis(c(0,365),
       axes=list("axesIntervals", labels=monthLetters) )
plot(yearbasis3.)

# set up the Fourier basis for the monthly temperature data,
#  using 9 basis functions with period 12 months.
monthbasis <- create.fourier.basis(c(0,12), 9, 12.0)

#  plot the basis
plot(monthbasis)

# Create a false Fourier basis using 1 basis function.
falseFourierBasis <- create.fourier.basis(nbasis=1)
#  plot the basis:  constant
plot(falseFourierBasis)
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