<s>
In	O
mathematics	O
,	O
the	O
Lehmer	B-Language
mean	I-Language
of	O
a	O
tuple	B-Application
of	O
positive	O
real	O
numbers	O
,	O
named	O
after	O
Derrick	O
Henry	O
Lehmer	O
,	O
is	O
defined	O
as	O
:	O
</s>
<s>
The	O
weighted	O
Lehmer	B-Language
mean	I-Language
with	O
respect	O
to	O
a	O
tuple	B-Application
of	O
positive	O
weights	O
is	O
defined	O
as	O
:	O
</s>
<s>
for	O
interpolating	B-Algorithm
between	O
minimum	O
and	O
maximum	O
via	O
arithmetic	O
mean	O
and	O
harmonic	O
mean	O
.	O
</s>
<s>
The	O
derivative	O
of	O
the	O
weighted	O
Lehmer	B-Language
mean	I-Language
is	O
:	O
</s>
<s>
Like	O
a	O
power	B-Language
mean	I-Language
,	O
a	O
Lehmer	B-Language
mean	I-Language
serves	O
a	O
non-linear	O
moving	O
average	O
which	O
is	O
shifted	O
towards	O
small	O
signal	O
values	O
for	O
small	O
and	O
emphasizes	O
big	O
signal	O
values	O
for	O
big	O
.	O
</s>
<s>
Given	O
an	O
efficient	O
implementation	O
of	O
a	O
moving	B-Algorithm
arithmetic	I-Algorithm
mean	I-Algorithm
called	O
you	O
can	O
implement	O
a	O
moving	O
Lehmer	B-Language
mean	I-Language
according	O
to	O
the	O
following	O
Haskell	B-Language
code	O
.	O
</s>
<s>
For	O
big	O
it	O
can	O
serve	O
an	O
envelope	B-Algorithm
detector	I-Algorithm
on	O
a	O
rectified	B-Algorithm
signal	O
.	O
</s>
<s>
Positive	O
Q	O
can	O
reduce	O
pepper	B-Algorithm
noise	I-Algorithm
and	O
negative	O
Q	O
can	O
reduce	O
salt	B-Algorithm
noise	I-Algorithm
.	O
</s>
