# fourier: Fourier Basis Function Values In fda: Functional Data Analysis

 fourier R Documentation

## 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)
``````

### 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.

### 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.

### 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.

`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)

``````

fda documentation built on May 29, 2024, 11:26 a.m.