<s>
In	O
mathematics	O
,	O
the	O
continuous	B-Algorithm
wavelet	I-Algorithm
transform	I-Algorithm
(	O
CWT	O
)	O
is	O
a	O
formal	O
(	O
i.e.	O
,	O
non-numerical	O
)	O
tool	O
that	O
provides	O
an	O
overcomplete	O
representation	O
of	O
a	O
signal	O
by	O
letting	O
the	O
translation	O
and	O
scale	O
parameter	O
of	O
the	O
wavelets	O
vary	O
continuously	O
.	O
</s>
<s>
To	O
recover	O
the	O
original	O
signal	O
,	O
the	O
first	O
inverse	O
continuous	B-Algorithm
wavelet	I-Algorithm
transform	I-Algorithm
can	O
be	O
exploited	O
.	O
</s>
<s>
is	O
admissible	O
constant	O
,	O
where	O
hat	O
means	O
Fourier	B-Algorithm
transform	I-Algorithm
operator	O
.	O
</s>
<s>
To	O
recover	O
the	O
original	O
signal	O
,	O
the	O
second	O
inverse	O
continuous	B-Algorithm
wavelet	I-Algorithm
transform	I-Algorithm
can	O
be	O
exploited	O
.	O
</s>
<s>
Such	O
defined	O
wavelet	O
can	O
be	O
called	O
as	O
an	O
analyzing	O
wavelet	O
,	O
because	O
it	O
admits	O
to	O
time-frequency	B-Algorithm
analysis	I-Algorithm
.	O
</s>
<s>
In	O
definition	O
,	O
the	O
continuous	B-Algorithm
wavelet	I-Algorithm
transform	I-Algorithm
is	O
a	O
convolution	B-Language
of	O
the	O
input	O
data	O
sequence	O
with	O
a	O
set	O
of	O
functions	O
generated	O
by	O
the	O
mother	O
wavelet	O
.	O
</s>
<s>
The	O
convolution	B-Language
can	O
be	O
computed	O
by	O
using	O
a	O
fast	O
Fourier	B-Algorithm
transform	I-Algorithm
(	O
FFT	O
)	O
algorithm	O
.	O
</s>
<s>
A	O
complex	O
mother	O
wavelet	O
will	O
convert	O
the	O
continuous	B-Algorithm
wavelet	I-Algorithm
transform	I-Algorithm
to	O
a	O
complex	O
valued	O
function	O
.	O
</s>
<s>
The	O
power	O
spectrum	O
of	O
the	O
continuous	B-Algorithm
wavelet	I-Algorithm
transform	I-Algorithm
can	O
be	O
represented	O
by	O
.	O
</s>
<s>
Moreover	O
,	O
wavelet	O
transforms	O
can	O
be	O
applied	O
to	O
the	O
following	O
scientific	O
research	O
areas	O
:	O
edge	O
and	O
corner	O
detection	O
,	O
partial	O
differential	O
equation	O
solving	O
,	O
transient	O
detection	O
,	O
filter	O
design	O
,	O
electrocardiogram	B-Application
(	O
ECG	B-Application
)	O
analysis	O
,	O
texture	O
analysis	O
,	O
business	O
information	O
analysis	O
and	O
gait	O
analysis	O
.	O
</s>
<s>
Wavelet	O
transforms	O
can	O
also	O
be	O
used	O
in	O
Electroencephalography	B-Application
(	O
EEG	B-Application
)	O
data	O
analysis	O
to	O
identify	O
epileptic	O
spikes	O
resulting	O
from	O
epilepsy	O
.	O
</s>
<s>
Continuous	B-Algorithm
Wavelet	I-Algorithm
Transform	I-Algorithm
(	O
CWT	O
)	O
is	O
very	O
efficient	O
in	O
determining	O
the	O
damping	O
ratio	O
of	O
oscillating	O
signals	O
(	O
e.g.	O
</s>
