fda (version 1.2.3)

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=width,  dropind=NULL, quadvals=NULL,
              values=NULL, longNames=TRUE)

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. Default value c(0,1)

nbasis

the number of basis functions, rounded up to the nearest odd integer. The number of basis functions is always odd, even when an even number is specified, so as to preserve the pairing of sine and cosine functions. Default value 3.

period

the width of any interval over which the Fourier functions repeat themselves, or are periodic. The default is the width of the interval defined in rangeval.

dropind

a vector of integers specifiying the basis functions to be dropped, if any. For example, if it is required that a function be zero at the left boundary, this is achieved by dropping the first basis function, the only one that is nonzero a

quadvals

a matrix with two columns and a number of rows equal to the number of argument values used to approximate an integral using Simpson's rule. The first column contains these argument values. A minimum of 5 values are required for each inter-kn

values

a list containing the basis functions and their derivatives evaluated at the quadrature points contained in the first column of quadvals.

longNames

if FALSE, the function value will include a component 'names', the first of which will be 'const', followed by 'sin1', 'cos1', 'sin2', ... .

if TRUE, the function value will include 'names' as when longNames = FALSE, but with the 'period

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

# Create a minimal Fourier basis for the monthly temperature data, 
#  using 3 basis functions with period 12 months.
monthbasis3 <- create.fourier.basis(c(0,12) )
#  plot the basis
plot(monthbasis3)

# 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)