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
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