<s>
In	O
sound	B-Algorithm
processing	I-Algorithm
,	O
the	O
mel-frequency	B-Algorithm
cepstrum	I-Algorithm
(	O
MFC	O
)	O
is	O
a	O
representation	O
of	O
the	O
short-term	O
power	O
spectrum	O
of	O
a	O
sound	O
,	O
based	O
on	O
a	O
linear	O
cosine	O
transform	O
of	O
a	O
log	O
power	O
spectrum	O
on	O
a	O
nonlinear	O
mel	B-Architecture
scale	I-Architecture
of	O
frequency	O
.	O
</s>
<s>
Mel-frequency	B-Algorithm
cepstral	I-Algorithm
coefficients	I-Algorithm
(	O
MFCCs	O
)	O
are	O
coefficients	O
that	O
collectively	O
make	O
up	O
an	O
MFC	O
.	O
</s>
<s>
They	O
are	O
derived	O
from	O
a	O
type	O
of	O
cepstral	B-Algorithm
representation	O
of	O
the	O
audio	O
clip	O
(	O
a	O
nonlinear	O
"	O
spectrum-of-a-spectrum	O
"	O
)	O
.	O
</s>
<s>
The	O
difference	O
between	O
the	O
cepstrum	B-Algorithm
and	O
the	O
mel-frequency	B-Algorithm
cepstrum	I-Algorithm
is	O
that	O
in	O
the	O
MFC	O
,	O
the	O
frequency	O
bands	O
are	O
equally	O
spaced	O
on	O
the	O
mel	B-Architecture
scale	I-Architecture
,	O
which	O
approximates	O
the	O
human	O
auditory	O
system	O
's	O
response	O
more	O
closely	O
than	O
the	O
linearly-spaced	O
frequency	O
bands	O
used	O
in	O
the	O
normal	O
spectrum	O
.	O
</s>
<s>
Take	O
the	O
Fourier	B-Algorithm
transform	I-Algorithm
of	O
(	O
a	O
windowed	O
excerpt	O
of	O
)	O
a	O
signal	O
.	O
</s>
<s>
Map	O
the	O
powers	O
of	O
the	O
spectrum	O
obtained	O
above	O
onto	O
the	O
mel	B-Architecture
scale	I-Architecture
,	O
using	O
triangular	O
overlapping	O
windows	O
or	O
alternatively	O
,	O
cosine	B-Algorithm
overlapping	I-Algorithm
windows	I-Algorithm
.	O
</s>
<s>
Take	O
the	O
discrete	B-General_Concept
cosine	I-General_Concept
transform	I-General_Concept
of	O
the	O
list	O
of	O
mel	O
log	O
powers	O
,	O
as	O
if	O
it	O
were	O
a	O
signal	O
.	O
</s>
<s>
There	O
can	O
be	O
variations	O
on	O
this	O
process	O
,	O
for	O
example	O
:	O
differences	O
in	O
the	O
shape	O
or	O
spacing	O
of	O
the	O
windows	O
used	O
to	O
map	O
the	O
scale	O
,	O
or	O
addition	O
of	O
dynamics	O
features	B-Algorithm
such	O
as	O
"	O
delta	O
"	O
and	O
"	O
delta-delta	O
"	O
(	O
first	O
-	O
and	O
second-order	O
frame-to-frame	O
difference	O
)	O
coefficients	O
.	O
</s>
<s>
Talking	O
about	O
speech	B-Application
recognition	I-Application
to	O
identify	O
mobile	O
phones	O
,	O
the	O
production	O
of	O
electronic	O
components	O
in	O
a	O
phone	O
have	O
tolerances	O
because	O
different	O
electronic	O
circuit	O
realizations	B-Application
do	O
not	O
have	O
exact	O
same	O
transfer	O
functions	O
.	O
</s>
<s>
The	O
dissimilarities	O
in	O
the	O
transfer	O
function	O
from	O
one	O
realization	B-Application
to	O
another	O
becomes	O
more	O
prominent	O
if	O
the	O
task	O
performing	O
circuits	O
are	O
from	O
different	O
manufacturers	O
.	O
</s>
<s>
Hence	O
,	O
each	O
cell	O
phone	O
introduces	O
a	O
convolutional	B-Language
distortion	O
on	O
input	O
speech	O
that	O
leaves	O
its	O
unique	O
impact	O
on	O
the	O
recordings	O
from	O
the	O
cell	O
phone	O
.	O
</s>
<s>
Hence	O
,	O
as	O
specified	O
the	O
footprint	O
of	O
mobile	O
phone	O
of	O
the	O
recorded	O
speech	O
is	O
the	O
convolution	B-Language
distortion	O
that	O
helps	O
to	O
identify	O
the	O
recording	O
phone	O
.	O
</s>
<s>
The	O
embedded	O
identity	O
of	O
the	O
cell	O
phone	O
requires	O
a	O
conversion	O
to	O
a	O
better	O
identifiable	O
form	O
,	O
hence	O
,	O
taking	O
short-time	O
Fourier	B-Algorithm
transform	I-Algorithm
:	O
</s>
<s>
Providing	O
importance	O
to	O
the	O
envelope	O
of	O
the	O
spectrum	O
which	O
multiplied	O
by	O
filter	O
bank	O
(	O
suitable	O
cepstrum	B-Algorithm
with	O
mel-scale	O
filter	O
bank	O
)	O
,	O
after	O
smoothing	O
filter	O
bank	O
with	O
transfer	O
function	O
U(f )	O
,	O
the	O
log	O
operation	O
on	O
output	O
energies	O
are	O
:	O
</s>
<s>
where	O
,	O
cy(j )	O
,	O
ce(j )	O
,	O
cw(j )	O
are	O
the	O
recorded	O
speech	O
cepstrum	B-Algorithm
and	O
weighted	O
equivalent	O
impulse	O
response	O
of	O
cell	O
phone	O
recorder	O
that	O
characterizes	O
the	O
cell	O
phone	O
,	O
respectively	O
,	O
while	O
j	O
is	O
the	O
number	O
of	O
filters	O
in	O
the	O
filter	O
bank	O
.	O
</s>
<s>
Commonly	O
used	O
window	O
functions	O
-	O
Hamming	O
and	O
Hanning	B-Algorithm
windows	I-Algorithm
.	O
</s>
<s>
MFCCs	O
are	O
obtained	O
by	O
taking	O
Discrete	B-General_Concept
Cosine	I-General_Concept
Transform	I-General_Concept
(	O
DCT	B-General_Concept
)	O
of	O
the	O
spectral	O
envelope	O
.	O
</s>
<s>
Cepstrum	B-Algorithm
coefficients	O
are	O
obtained	O
as	O
:	O
</s>
<s>
MFCCs	O
are	O
commonly	O
used	O
as	O
features	B-Algorithm
in	O
speech	B-Application
recognition	I-Application
systems	O
,	O
such	O
as	O
the	O
systems	O
which	O
can	O
automatically	O
recognize	O
numbers	O
spoken	O
into	O
a	O
telephone	O
.	O
</s>
<s>
MFCCs	O
are	O
also	O
increasingly	O
finding	O
uses	O
in	O
music	B-Application
information	I-Application
retrieval	I-Application
applications	O
such	O
as	O
genre	O
classification	O
,	O
audio	O
similarity	O
measures	O
,	O
etc	O
.	O
</s>
<s>
MFCC	O
values	O
are	O
not	O
very	O
robust	O
in	O
the	O
presence	O
of	O
additive	O
noise	O
,	O
and	O
so	O
it	O
is	O
common	O
to	O
normalise	O
their	O
values	O
in	O
speech	B-Application
recognition	I-Application
systems	O
to	O
lessen	O
the	O
influence	O
of	O
noise	O
.	O
</s>
<s>
Some	O
researchers	O
propose	O
modifications	O
to	O
the	O
basic	O
MFCC	O
algorithm	O
to	O
improve	O
robustness	O
,	O
such	O
as	O
by	O
raising	O
the	O
log-mel-amplitudes	O
to	O
a	O
suitable	O
power	O
(	O
around	O
2	O
or	O
3	O
)	O
before	O
taking	O
the	O
discrete	B-General_Concept
cosine	I-General_Concept
transform	I-General_Concept
(	O
DCT	B-General_Concept
)	O
,	O
which	O
reduces	O
the	O
influence	O
of	O
low-energy	O
components	O
.	O
</s>
<s>
We	O
will	O
,	O
therefore	O
,	O
call	O
these	O
the	O
mel-based	O
cepstral	B-Algorithm
parameters	O
.	O
</s>
<s>
Many	O
authors	O
,	O
including	O
Davis	O
and	O
Mermelstein	O
,	O
have	O
commented	O
that	O
the	O
spectral	O
basis	O
functions	O
of	O
the	O
cosine	O
transform	O
in	O
the	O
MFC	O
are	O
very	O
similar	O
to	O
the	O
principal	B-Application
components	I-Application
of	O
the	O
log	O
spectra	O
,	O
which	O
were	O
applied	O
to	O
speech	O
representation	O
and	O
recognition	O
much	O
earlier	O
by	O
Pols	O
and	O
his	O
colleagues	O
.	O
</s>
