Fundamentals of Digital Image Processing - Control of Color Imaging Systems: Analysis and Design - page 72

2

Ideal

1.5

Linear
interpolation

1

0.5

0

0 0.5 1 1.5

ω

2 2.5 3

FIGURE 2.38 Frequency response of ideal and linear interpolation filters for P ¼ 2.

For P ¼ 2 and P ¼ 3, the filters are

h ( n ) ¼

1
2

1
2

and

h ( n ) ¼

1
3

2
3

2
3

1
3

( : )

1 1 2 119

The frequency response of the interpolation filter for P ¼ 2 is shown in Figure 2.38.

For downsampling by a factor of Q, the same filter can be used except that the

DC gain of the filter should be one. Therefore,

1
Q

1
Q

2
Q

Q 1 Q 1

Q

2
Q

1
Q

h ( n ) ¼ 1 ( 2 : 120 )

Q

Example 2.15

Given a 4 4 sequence

2
4

3
5

2312
4135
2412
2132

f (n, m) ¼

upsample the sequence f (n, m) by a factor of 2 using linear interpolation.

S OLUTION
We first insert zeros between pixels and increase the size to 8 8.