Image Processing Reference
In-Depth Information
n
n
xn Ae
cos
n
;
xn Ae
sin
n
.
(3)
0
0
R
0
I
0
Clearly,
x
R
(
n
) and
x
I
(
n
) are real discrete-time sinusoidal signals whose amplitude A
e
o
n
is
constant (
0
=0), increasing (
0
>0) or decreasing
0
<0) exponents (Fig. 1).
Real part
Imaginary part
60
0.5
0.4
50
0.3
40
0.2
0.1
30
0
-0.1
20
-0.2
10
-0.3
-0.4
0.
0
0.5
0.4
0.2
0
0
-0.5
-0.2
-0 4
0
10
20
30
40
50
60
-0.5
Real part
Imaginary part
Sample number
(a)
100
60
Real part
Imaginary part
80
50
60
40
40
30
20
20
0
10
-20
-40
15
0
150
100
100
50
50
0
0
-50
-50
-100
-100
Imaginary part
Real part
-60
0
10
20
30
40
50
60
Sample number
(b)
0.8
Real part
Imaginary part
60
0.6
50
0.4
0
0.2
30
0
20
-0.2
10
-0.4
0.
0
0.5
0.
0.2
0
0
0.2
-0.
-0.5
Real part
0
10
20
30
40
50
60
Imaginary part
Sample number
(c)
Fig. 1. Complex exponential signal
x
(
n
) and its real and imaginary components
x
R
(
n
) and
x
I
(
n
) for (a)
0
=-0.085; (b)
0
=0.085 and (c)
0
=0