<s>
Prony	B-Algorithm
analysis	I-Algorithm
(	O
Prony	B-Algorithm
's	I-Algorithm
method	I-Algorithm
)	O
was	O
developed	O
by	O
Gaspard	O
Riche	O
de	O
Prony	O
in	O
1795	O
.	O
</s>
<s>
Similar	O
to	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
,	O
Prony	B-Algorithm
's	I-Algorithm
method	I-Algorithm
extracts	O
valuable	O
information	O
from	O
a	O
uniformly	O
sampled	O
signal	O
and	O
builds	O
a	O
series	O
of	O
damped	O
complex	O
exponentials	O
or	O
damped	O
sinusoids	O
.	O
</s>
<s>
Prony	B-Algorithm
's	I-Algorithm
method	I-Algorithm
is	O
essentially	O
a	O
decomposition	O
of	O
a	O
signal	O
with	O
complex	O
exponentials	O
via	O
the	O
following	O
process	O
:	O
</s>
<s>
The	O
key	O
to	O
Prony	B-Algorithm
's	I-Algorithm
Method	I-Algorithm
is	O
that	O
the	O
coefficients	O
in	O
the	O
difference	O
equation	O
are	O
related	O
to	O
the	O
following	O
polynomial	O
:	O
</s>
<s>
These	O
facts	O
lead	O
to	O
the	O
following	O
three	O
steps	O
within	O
Prony	B-Algorithm
's	I-Algorithm
Method	I-Algorithm
:	O
</s>
<s>
This	O
leads	O
to	O
the	O
same	O
Nyquist	O
sampling	O
criteria	O
that	O
discrete	O
Fourier	B-Algorithm
transforms	I-Algorithm
are	O
subject	O
to	O
:	O
</s>
