Biomedical Engineering Reference
In-Depth Information
(13.17) and (13.18).
W
r
N
X
m
(
q
)
X
m
+1
(
p
)
=
X
m
(
p
)
+
(13.17)
W
r
N
X
m
(
q
)
X
m
+1
(
q
)
=
X
m
(
p
)
−
(13.18)
Bit Reversal
: To perform the computation as shown in the Fig. 13.4 flow graph, the
input data must be stored in a nonsequential order and is known as the bit-reverse order.
For a sequence of
N
=
8, the input data are represented in binary form as
LSB
=
0
X
(0)
=
X
(0
,
0
,
0)
X
(4)
=
X
(1
,
0
,
0)
X
(2)
=
X
(0
,
1
,
0)
X
(6)
=
X
(1
,
1
,
0)
LSB
=
1
X
(1)
=
X
(0
,
0
,
1)
X
(5)
=
X
(1
,
0
,
1)
X
(3)
=
X
(0
,
1
,
1)
X
(7)
=
X
(1
,
1
,
1)
Upon observation, one can see that the bits (LSB
=
0) of the top section are all
even number samples; and LSB
1 of bottom section are all odd number samples,
which are obtained by writing the signal sequences in binary form and bit-reversing each
to get the new order. If the input is not bit-reversed, then the output will need to be
bit-reversed. The flow graph can be arranged in such a way that both input and output
need not be bit-reversed.
=
13.6 DECIMATION-IN-FREQUENCY
The configuration is obtained by dividing the output sequence into smaller and smaller
subsequences. Here the input sequence is divided into first or second halves. Accord-
ing to Fourier integral theorem, a function must satisfy the Dirichlet conditions or
every finite interval and the integral from infinity to negative infinity is finite. The
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