<s>
In	O
computational	O
mathematics	O
,	O
the	O
Hadamard	O
ordered	O
fast	B-Algorithm
Walsh	I-Algorithm
–	I-Algorithm
Hadamard	I-Algorithm
transform	I-Algorithm
(	O
FWHTh	O
)	O
is	O
an	O
efficient	O
algorithm	O
to	O
compute	O
the	O
Walsh	B-Algorithm
–	I-Algorithm
Hadamard	I-Algorithm
transform	I-Algorithm
(	O
WHT	O
)	O
.	O
</s>
<s>
The	O
FWHTh	O
is	O
a	O
divide-and-conquer	B-Algorithm
algorithm	I-Algorithm
that	O
recursively	O
breaks	O
down	O
a	O
WHT	O
of	O
size	O
into	O
two	O
smaller	O
WHTs	O
of	O
size	O
.	O
</s>
<s>
The	O
sequency-ordered	B-Algorithm
,	O
also	O
known	O
as	O
Walsh-ordered	O
,	O
fast	B-Algorithm
Walsh	I-Algorithm
–	I-Algorithm
Hadamard	I-Algorithm
transform	I-Algorithm
,	O
FWHTw	O
,	O
is	O
obtained	O
by	O
computing	O
the	O
FWHTh	O
as	O
above	O
,	O
and	O
then	O
rearranging	O
the	O
outputs	O
.	O
</s>
<s>
A	O
simple	O
fast	O
nonrecursive	O
implementation	O
of	O
the	O
Walsh	B-Algorithm
–	I-Algorithm
Hadamard	I-Algorithm
transform	I-Algorithm
follows	O
from	O
decomposition	O
of	O
the	O
Hadamard	B-Algorithm
transform	I-Algorithm
matrix	O
as	O
,	O
where	O
A	O
is	O
m-th	O
root	O
of	O
.	O
</s>
