Specifications

Intel
®
Image Processing Library Reference Manual
7-2
7
The function iplRealFft2D() transforms a 2D image and produces the
Fourier coefficients in the
RCPack2D format. To complement this, function
iplCcsFft2D() is provided that uses its input in RCPack2D format,
performs the Fourier transform, and produces its output as a real 2D image.
The functions
iplRealFft2D() and iplCcsFft2D() together can be used
to perform frequency domain filtering of images.
RCPack2D format is defined based on the following Fourier transform
equations:
Af
ijl
L
iks
K
sj
l
L
kl
k
K
,,
exp exp=−






−






=
−
=
−
∑∑
0
1
0
1
22ππ
f
LK
A
ijl
L
iks
K
kl sj
s
K
j
L
,,
exp exp=












=
−
=
−
∑∑
122
0
1
0
1
ππ
where i =−1 , f
k,l
is the pixel value in the k-th row and l-th column.
Note that the Fourier coefficients have the following relationship:
A
s,j
= conj(A
K-s, L-j
) s =1,..., K-1; j =1,..., L-1;
A
0,j
=conj(A
0,L-j
) j =1,..., L-1;
A
s,0
= conj(A
K-s, 0
) s =1,..., K-1.
Hence, to reconstruct the
L*K complex coefficients A
s,j
, it is enough to store
only L * K real values. The Fourier transform functions actually use
s =0,..., K-1; j =0,..., L/2.
Other Fourier coefficients can be found using complex-conjugate relations.
Fourier coefficients A
s,j
canbestoredintheRCPack2D format, which is a
convenient compact representation of a complex conjugate-symmetric
sequence. In the
RCPack2D format, the output samples of the FFT are
arranged as shown in Tables 7-2 and 7-3, where Re corresponds to Real
and Im corresponds to Imaginary. Table 7-4 is an example of output
samples storage for K =4andL =4.