Fast Fourier Transforms on Motorola's Digital Signal Processors

X=A+jB
Y=C+jD
X’=A+C+j(D+B)
-
Y’=A-C+j(D-B)
X=A+jC
W
Y=B+jD
6.1.2 Reordering
X’=A+BWr+DWi
+j(C+DWr-BWi)
Y’=A-(BWr+DWi)
-j[C+(DWr-BWi)]
The output order of the Bergland algorithm is slightly
different than the bit-reversed order, and the
twiddle factor required in the calculation is also in
Bergland order. To get this special order, one may
use the following algorithm for doubling the length
of each number sequence:
1. Multiply the second entry of the sequence by
two, and make this product the second entry of
the new sequence
2. Subtract each nonzero entry of the sequence
from twice the product formed in step 1 (these
differences form the rest of the even entries of
the new sequence)
3. Take the odd entries of the new sequence as
the numbers of the original sequence
6-6 MOTOROLA
*
* -
* denotes conjugate
(a) (b)
Figure 6-3 (a) Butterfly of Bergland Algorithm with W = 1
(b) Butterfly of Bergland Algorithm with W ≠ 1
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