<s>
In	O
digital	B-General_Concept
signal	I-General_Concept
processing	I-General_Concept
,	O
half-band	B-Algorithm
filters	I-Algorithm
are	O
widely	O
used	O
for	O
their	O
efficiency	O
in	O
multi-rate	O
applications	O
.	O
</s>
<s>
A	O
half-band	B-Algorithm
filter	I-Algorithm
is	O
a	O
low-pass	B-Algorithm
filter	I-Algorithm
that	O
reduces	O
the	O
maximum	O
bandwidth	O
of	O
sampled	O
data	O
by	O
a	O
factor	O
of	O
2	O
(	O
one	O
octave	O
)	O
.	O
</s>
<s>
When	O
multiple	O
octaves	O
of	O
reduction	O
are	O
needed	O
,	O
a	O
cascade	O
of	O
half-band	B-Algorithm
filters	I-Algorithm
is	O
common	O
.	O
</s>
<s>
And	O
when	O
the	O
goal	O
is	O
downsampling	B-Algorithm
,	O
each	O
half-band	B-Algorithm
filter	I-Algorithm
needs	O
to	O
compute	O
only	O
half	O
as	O
many	O
output	O
samples	O
as	O
input	O
samples	O
.	O
</s>
<s>
It	O
follows	O
from	O
the	O
filter	O
's	O
definition	O
that	O
its	O
transition	B-Algorithm
region	I-Algorithm
,	O
or	O
skirt	O
,	O
can	O
be	O
centered	O
at	O
frequency	O
where	O
is	O
the	O
input	O
sample-rate	O
.	O
</s>
