<s>
A	O
phase	B-Application
vocoder	I-Application
is	O
a	O
type	O
of	O
vocoder-purposed	O
algorithm	O
which	O
can	O
interpolate	B-Algorithm
information	O
present	O
in	O
the	O
frequency	O
and	O
time	O
domains	O
of	O
audio	O
signals	O
by	O
using	O
phase	O
information	O
extracted	O
from	O
a	O
frequency	O
transform	O
.	O
</s>
<s>
At	O
the	O
heart	O
of	O
the	O
phase	B-Application
vocoder	I-Application
is	O
the	O
short-time	B-Algorithm
Fourier	I-Algorithm
transform	I-Algorithm
(	O
STFT	B-Algorithm
)	O
,	O
typically	O
coded	O
using	O
fast	O
Fourier	O
transforms	O
.	O
</s>
<s>
The	O
STFT	B-Algorithm
converts	O
a	O
time	O
domain	O
representation	O
of	O
sound	O
into	O
a	O
time-frequency	O
representation	O
(	O
the	O
"	O
analysis	O
"	O
phase	O
)	O
,	O
allowing	O
modifications	O
to	O
the	O
amplitudes	O
or	O
phases	O
of	O
specific	O
frequency	O
components	O
of	O
the	O
sound	O
,	O
before	O
resynthesis	O
of	O
the	O
time-frequency	O
domain	O
representation	O
into	O
the	O
time	O
domain	O
by	O
the	O
inverse	O
STFT	B-Algorithm
.	O
</s>
<s>
The	O
main	O
problem	O
that	O
has	O
to	O
be	O
solved	O
for	O
all	O
cases	O
of	O
manipulation	O
of	O
the	O
STFT	B-Algorithm
is	O
the	O
fact	O
that	O
individual	O
signal	O
components	O
(	O
sinusoids	O
,	O
impulses	O
)	O
will	O
be	O
spread	O
over	O
multiple	O
frames	O
and	O
multiple	O
STFT	B-Algorithm
frequency	O
locations	O
(	O
bins	O
)	O
.	O
</s>
<s>
This	O
is	O
because	O
the	O
STFT	B-Algorithm
analysis	O
is	O
done	O
using	O
overlapping	O
analysis	B-Language
windows	I-Language
.	O
</s>
<s>
The	O
windowing	O
results	O
in	O
spectral	O
leakage	O
such	O
that	O
the	O
information	O
of	O
individual	O
sinusoidal	O
components	O
is	O
spread	O
over	O
adjacent	O
STFT	B-Algorithm
bins	O
.	O
</s>
<s>
To	O
avoid	O
border	O
effects	O
of	O
tapering	O
of	O
the	O
analysis	B-Language
windows	I-Language
,	O
STFT	B-Algorithm
analysis	B-Language
windows	I-Language
overlap	O
in	O
time	O
.	O
</s>
<s>
This	O
time	O
overlap	O
results	O
in	O
the	O
fact	O
that	O
adjacent	O
STFT	B-Algorithm
analyses	O
are	O
strongly	O
correlated	O
(	O
a	O
sinusoid	O
present	O
in	O
analysis	O
frame	O
at	O
time	O
"	O
t	O
"	O
will	O
be	O
present	O
in	O
the	O
subsequent	O
frames	O
as	O
well	O
)	O
.	O
</s>
<s>
The	O
problem	O
of	O
signal	O
transformation	O
with	O
the	O
phase	B-Application
vocoder	I-Application
is	O
related	O
to	O
the	O
problem	O
that	O
all	O
modifications	O
that	O
are	O
done	O
in	O
the	O
STFT	B-Algorithm
representation	O
need	O
to	O
preserve	O
the	O
appropriate	O
correlation	O
between	O
adjacent	O
frequency	O
bins	O
(	O
vertical	O
coherence	O
)	O
and	O
time	O
frames	O
(	O
horizontal	O
coherence	O
)	O
.	O
</s>
<s>
Except	O
in	O
the	O
case	O
of	O
extremely	O
simple	O
synthetic	O
sounds	O
,	O
these	O
appropriate	O
correlations	O
can	O
be	O
preserved	O
only	O
approximately	O
,	O
and	O
since	O
the	O
invention	O
of	O
the	O
phase	B-Application
vocoder	I-Application
research	O
has	O
been	O
mainly	O
concerned	O
with	O
finding	O
algorithms	O
that	O
would	O
preserve	O
the	O
vertical	O
and	O
horizontal	O
coherence	O
of	O
the	O
STFT	B-Algorithm
representation	O
after	O
the	O
modification	O
.	O
</s>
<s>
The	O
phase	B-Application
vocoder	I-Application
was	O
introduced	O
in	O
1966	O
by	O
Flanagan	O
as	O
an	O
algorithm	O
that	O
would	O
preserve	O
horizontal	O
coherence	O
between	O
the	O
phases	O
of	O
bins	O
that	O
represent	O
sinusoidal	O
components	O
.	O
</s>
<s>
This	O
original	O
phase	B-Application
vocoder	I-Application
did	O
not	O
take	O
into	O
account	O
the	O
vertical	O
coherence	O
between	O
adjacent	O
frequency	O
bins	O
,	O
and	O
therefore	O
,	O
time	O
stretching	O
with	O
this	O
system	O
did	O
produce	O
sound	O
signals	O
that	O
were	O
missing	O
clarity	O
.	O
</s>
<s>
The	O
optimal	O
reconstruction	O
of	O
the	O
sound	O
signal	O
from	O
STFT	B-Algorithm
after	O
amplitude	O
modifications	O
has	O
been	O
proposed	O
by	O
Griffin	O
and	O
Lim	O
in	O
1984	O
.	O
</s>
<s>
This	O
algorithm	O
does	O
not	O
consider	O
the	O
problem	O
of	O
producing	O
a	O
coherent	O
STFT	B-Algorithm
,	O
but	O
it	O
does	O
allow	O
finding	O
the	O
sound	O
signal	O
that	O
has	O
an	O
STFT	B-Algorithm
that	O
is	O
as	O
close	O
as	O
possible	O
to	O
the	O
modified	O
STFT	B-Algorithm
even	O
if	O
the	O
modified	O
STFT	B-Algorithm
is	O
not	O
coherent	O
(	O
does	O
not	O
represent	O
any	O
signal	O
)	O
.	O
</s>
<s>
The	O
proposition	O
of	O
Laroche	O
and	O
Dolson	O
has	O
to	O
be	O
seen	O
as	O
a	O
turning	O
point	O
in	O
phase	B-Application
vocoder	I-Application
history	O
.	O
</s>
<s>
An	O
example	O
of	O
software	O
implementation	O
of	O
phase	B-Application
vocoder	I-Application
based	O
signal	O
transformation	O
using	O
means	O
similar	O
to	O
those	O
described	O
here	O
to	O
achieve	O
high	O
quality	O
signal	O
transformation	O
is	O
Ircam	O
's	O
SuperVP	O
.	O
</s>
<s>
British	O
composer	O
Trevor	O
Wishart	O
used	O
phase	B-Application
vocoder	I-Application
analyses	O
and	O
transformations	O
of	O
a	O
human	O
voice	O
as	O
the	O
basis	O
for	O
his	O
composition	O
Vox	O
5	O
(	O
part	O
of	O
his	O
larger	O
Vox	O
Cycle	O
)	O
.	O
</s>
<s>
Transfigured	O
Wind	O
by	O
American	O
composer	O
Roger	O
Reynolds	O
uses	O
the	O
phase	B-Application
vocoder	I-Application
to	O
perform	O
time-stretching	O
of	O
flute	O
sounds	O
.	O
</s>
<s>
The	O
music	O
of	O
JoAnn	O
Kuchera-Morin	O
makes	O
some	O
of	O
the	O
earliest	O
and	O
most	O
extensive	O
use	O
of	O
phase	B-Application
vocoder	I-Application
transformations	O
,	O
such	O
as	O
in	O
Dreampaths	O
(	O
1989	O
)	O
.	O
</s>
