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, 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 ,