Digital Signal Processing Reference
In-Depth Information
Stage 1
()
+
()
=+ =Æ
()
xWx
0
0
4
1
0
1
x
0
()
-
()
=-=Æ
()
x
0
Wx
0
4
1
0
1
x
4
()
+
()
=+ =Æ
()
0
x
2
Wx
6
1
0
1
x
2
()
-
()
=-=Æ
()
x
2
Wx
0
6
1
0
1
x
6
()
+
()
=+ =Æ
()
xWx
1
0
5
1
0
1
x
1
(()
-
()
=-=Æ
()
0
x
1
Wx
5101
x
5
()
+
()
=+ =Æ
()
xWx
3
0
7
1
0
1
x
3
()
-
()
=-=Æ
()
xWx
3
0
7
1
0
1
x
7
s represents the intermediate output after the first iteration
and becomes the input to the subsequent stage.
where the sequence
x
¢
Stage 2
¢
()
+¢
()
=+= Æ≤
()
¢
()
+¢
()
=+
()
=-Æ≤
()
¢
()
-¢
()
=-=Æ≤
()
¢
()
-¢
()
=-
()
=+Æ≤
()
¢
()
+
0
x
0
Wx
2
1
1
2
x
0
x
4
Wx
2
6
1
j
1
j
x
4
x
0
Wx
0
2
1
1
0
x
2
2
x
4
Wx
6
1
j
1
j
x
6
¢
()
=+= Æ≤
()
¢
()
+¢
()
=+
( ()
=-Æ≤
()
¢
()
-¢
()
=-=Æ≤
()
¢
()
-¢
()
=-
( ()
=+Æ≤
()
x
1
W
0
x
3112
x
1
2
x
5
Wx
7
1
j
1
1
j
x
5
x
1
Wx
0
3
1
1
0
x
3
x
5
Wx
2
7
1
j
1
1
j
x
7
where the intermediate second-stage output sequence
x
≤
s becomes the input
sequence to the final stage.
Stage 3
()
=≤
()
+≤
()
=
()
=≤
()
+≤
()
=-
()
=≤
()
+≤
()
=
()
=≤
()
+≤
()
=-
()
=≤
()
-≤
()
=
()
=≤
Xx
0
0
Wx
0
1
4
1
Xx
1
4
Wx
5
1
j
2 414
.
Xx
2
2
Wx
2
3
0
3
Xx
3
6
Wx
710 4
j
.
Xx
4
0
Wx
0
1
0
()
-≤
()
=+
()
=≤
()
-≤
()
=
()
=≤
()
-≤
()
=+
Xx
5
44
Wx
1
510 4
j
.
2
Xx
6
2
Wx
3
0
Xx
7
6
Wx
3
712 4
j
.
which is the same output sequence found in Exercise 6.1.
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