# fourierbasis

From spatstat v1.44-0
by Adrian Baddeley

##### Fourier Basis Functions

Evaluates the Fourier basis functions on a $d$-dimensional box with $d$-dimensional frequencies $k_i$ at the $d$-dimensional coordinates $x_j$.

##### Usage

`fourierbasis(x, k, win = boxx(rep(list(0:1), ncol(k))))`

##### Arguments

- x
- Coordinates.
A
`data.frame`

or matrix with $m$ rows and $d$ columns giving the $d$-dimensional coordinates. - k
- Frequencies.
A
`data.frame`

or matrix with $n$ rows and $d$ columns giving the frequencies of the Fourier-functions. - win
- window (of class
`"owin"`

,`"box3"`

or`"boxx"`

) giving the $d$-dimensional box domain of the Fourier functions.

##### Details

The result is an $n$ by $m$ matrix where the $(i,j)$'th
entry is the $d$-dimensional Fourier basis function with
frequency $k_i$ evaluated at the point $x_j$, i.e.,
$$\frac{1}{|W|}
\exp(2\pi i `x`

are contained in the given box.
Actually the box is only
used to determine the volume of the domain for normalization.

##### Value

- An
`n`

by`m`

matrix of complex values.

##### Examples

```
## 27 rows of three dimensional Fourier frequencies:
k <- expand.grid(-1:1,-1:1, -1:1)
## Two random points in the three dimensional unit box:
x <- rbind(runif(3),runif(3))
## 27 by 2 resulting matrix:
v <- fourierbasis(x, k)
head(v)
```

*Documentation reproduced from package spatstat, version 1.44-0, License: GPL (>= 2)*

### Community examples

Looks like there are no examples yet.