fft2

Scilab Function
Last update : 09/02/2006

fft2 - two-dimension fast Fourier transform

### Calling Sequence

  `y=fft2(x)`
  `y=fft2(x,n,m)`

### Parameters

- `x` : a vector/matrix/array (Real or Complex)
- `y` : a vector/matrix/array (Real or Complex)
- `m` : integer, number of rows.
- `n` : integer, number of columns.

### Description

    This functions performs the two-dimension discrete Fourier
        transform.

`y=fft2(x)` : y and x have the same size

`y=fft2(x,m,n):` If `m` (respectively `n` ) is less than the rows number (respectively columns) of `x` then the `x` rows number (resp. columns) is truncated, else if m (resp. `n` ) is more than the rows number (resp. columns) of `x` then `x` rows are completed by zero (resp. columns) .

if `x` is a matrix then `y` is a matrix, if `x` is a hypermatrix then `y` is a hypermatrix, with the size of the first dimension of `y` is equal to `m` , the size of the second dimension of `y` is equal to `n` , the size of the ith dimension of `y` (for i>2, case hypermatrix) equal to the size of the ith dimension of `x` . (i.e size(y,1)=m, size(y,2)=n and size(y,i)=size(x,i) for i>2)

### Examples

    //Comparison with explicit formula
    a=[1 2 3 ;4 5 6 ;7 8 9 ;10 11 12]
    m=size(a,1)
    n=size(a,2)
    // fourier transform along the rows
    for i=1:n
    a1(:,i)=exp(-2*%i*%pi*(0:m-1)'.*.(0:m-1)/m)*a(:,i)
    end
    // fourier transform along the columns
    for j=1:m
    a2temp=exp(-2*%i*%pi*(0:n-1)'.*.(0:n-1)/n)*(a1(j,:)).'
    a2(j,:)=a2temp.'
    end
    norm(a2-fft2(a))

### See Also

`fft` ,