Fundamentals of Digital Image Processing - Control of Color Imaging Systems: Analysis and Design - page 52

2
4

3
5 !

2
4

3
5

1240
1320
3140
0000

21 5 j69 5 þj6

2 - D DFT

1 j6 5 31 þj2

fi (n,m)

F(k, l)

¼ ¼

9 39 3

1 þj61 j2 3 5

c. Zero-pad the signal h(n, m) and compute its DFT

2
4

3
5 !

2
4

3
5

1300
2100
0000
0000

73 j4 13 þj4

2 - D DFT

4 j3 j5 2 j 2 þj

h(n,m)

H(k, l)

¼ ¼

1 1 j2 3 1 þj2

4 þj32 j 2 þj j5

d. Multiply the 2 DFTs

2
4

3
5

147 39 þ j29 39 j2

22 j21 j25 6 þ j3 j5

G(k, l)

¼ F(k, l) H(k, l) ¼

9 3 þ j6 27 3 j6

22 þ j21 j56 j3 j25

e. Take the inverse DFT of G(k, l)

2
4

3
5

1 5 10 12
3112110
5171414
6594

g(n, m) ¼ IDFT[G(k, l)] ¼

In practice, it may not be practical to compute DFT if the DFT size is large. In this
case, block convolution can be employed. As an example, consider designing a
convolver for ltering an image f of size MM by an finite impulse response (FIR)

lter of size L L, using FFT hardware capable of performing 1-D N-point FFT. We

rst divide the image data into blocks of size BB, where B ¼ NLþ 1, as shown

( B ) 2 of such image blocks.

in Figure 2.22. There are approximately N B ¼

M

f 1

f 2

...

B

f i

...

f i ( n, m )

M B

The i ith block

...

f ( n , m )

FIGURE 2.22 Dividing the image into subimages.