<s>
In	O
signal	O
processing	O
,	O
nonlinear	O
multidimensional	B-Algorithm
signal	I-Algorithm
processing	I-Algorithm
(	O
NMSP	O
)	O
covers	O
all	O
signal	O
processing	O
using	O
nonlinear	O
multidimensional	B-Algorithm
signals	I-Algorithm
and	O
systems	O
.	O
</s>
<s>
Nonlinear	O
multidimensional	B-Algorithm
signal	I-Algorithm
processing	I-Algorithm
is	O
a	O
subset	O
of	O
signal	O
processing	O
(	O
multidimensional	B-Algorithm
signal	I-Algorithm
processing	I-Algorithm
)	O
.	O
</s>
<s>
Nonlinear	O
systems	O
cannot	O
be	O
treated	O
as	O
linear	O
systems	O
,	O
using	O
Fourier	B-Algorithm
transformation	I-Algorithm
and	O
wavelet	O
analysis	O
.	O
</s>
<s>
But	O
there	O
are	O
some	O
efforts	O
to	O
characterize	O
nonlinear	O
systems	O
,	O
such	O
as	O
Volterra	B-Algorithm
and	O
Wiener	B-Algorithm
series	I-Algorithm
using	O
polynomial	O
integrals	O
as	O
the	O
use	O
of	O
those	O
methods	O
naturally	O
extend	O
the	O
signal	O
into	O
multi-dimensions	O
.	O
</s>
<s>
Another	O
example	O
is	O
the	O
Empirical	O
mode	O
decomposition	O
method	O
using	O
Hilbert	B-Algorithm
transform	I-Algorithm
instead	O
of	O
Fourier	B-Algorithm
Transform	I-Algorithm
for	O
nonlinear	O
multi-dimensional	O
systems	O
.	O
</s>
<s>
A	O
linear	O
frequency	O
response	O
function	O
(	O
FRF	O
)	O
can	O
be	O
extended	O
to	O
a	O
nonlinear	O
system	O
by	O
evaluation	O
of	O
higher	O
order	O
transfer	O
functions	O
and	O
impulse	O
response	O
functions	O
by	O
Volterra	B-Algorithm
series	I-Algorithm
.	O
</s>
<s>
Schetzen	O
suggested	O
the	O
definition	O
of	O
th	O
output	O
component	O
as	O
time	O
variables	O
so	O
as	O
to	O
permit	O
the	O
application	O
of	O
the	O
-dimensional	O
Fourier	B-Algorithm
transform	I-Algorithm
,	O
</s>
<s>
Taking	O
the	O
inverse	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
and	O
and	O
equalizing	O
,	O
we	O
obtain	O
the	O
following	O
equation	O
,	O
</s>
<s>
One	O
example	O
of	O
nonlinear	O
filters	O
is	O
the	O
(	O
generalized	O
directional	O
distance	O
rational	O
hybrid	O
filter	O
(	O
GDDRHF	O
)	O
)	O
for	O
multidimensional	B-Algorithm
signal	I-Algorithm
processing	I-Algorithm
.	O
</s>
