Scilab 6.0.0
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See the recommended documentation of this function

fft2

two-dimension fast Fourier transform

Syntax

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

Arguments

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))```