Digital Signal Processing Reference
In-Depth Information
a
(0
a
(1
a
()
X
(0
X
()
x
(0
x
(1
N
2
-point
2
X
()
2
a
(3
b
(0
b
(1
b
()
x
()
2
4
X
(6
X
(1
X
(3
X
(5
X
()
DFT
x
(3
x
()
W
N
0
W
N
1
W
N
2
W
N
3
4
x
(5
x
(6
x
()
1
1
1
1
N
2
-point
2
b
(3
DFT
7
7
FIGURE 4.32
The first iteration of the eight-point FFT.
z
y
x
x
x
zwx
x
w
y
y
z
y
1
x
FIGURE 4.33
Definitions of the graphical operations.
N
4
X
(0
X
()
x
(0
x
(1
- point
DFT
4
X
()
W
N
0
x
()
2
2
X
(6
X
(1
X
(5
X
(3
X
()
N
4
1
1
W
N
2
- point
DFT
x
(3
x
()
W
N
0
W
N
1
W
N
2
W
N
3
4
x
(5
x
(6
x
()
N
4
1
1
1
1
- point
DFT
W
N
0
N
4
- point
DFT
1
1
W
N
2
7
7
FIGURE 4.34
The second iteration of the eight-point FFT.
x
(0
x
(1
X
(0
X
()
W
N
0
4
X
()
1
W
N
0
x
()
2
2
X
(6
X
(1
X
(5
X
(3
X
1
1
W
N
2
W
N
0
x
(3
W
N
0
W
N
1
W
N
2
W
N
3
1
x
4
x
(5
x
(6
x
()
()
1
1
1
1
W
N
0
1
W
N
0
1
1
W
N
2
W
N
0
7
()
7
1
FIGURE 4.35
Block diagram for the eight-point FFT (total 12 multiplications).
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