The sequency-ordered Walsh-Hadamard transform (, also called Walsh
ordered
) can be obtained by first carrying out the fast
and then
reordering the components of
as shown above. Alternatively, we can
use the following fast
directly with better efficiency.
The sequency ordered WHT of can also be defined as
In the following, we assume
, and we represent
and
in binary form as, respectively,
and
, i.e.,
As the first step of the algorithm, we rearrange the order of the samples
by bit-reversal to get
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(11) |
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(12) |
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(13) |
Summarizing the above steps, we get the fast algorithm composed of
the bit-reversal and the three equations (11), (12), and (13), as illustrated
below: