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HST.582J / 6.555J / 16.456J Biomedical Signal and Image Processing
Spring 2007
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View Full DocumentHarvardMIT Division of Health Sciences and Technology
HST.582J: Biomedical Signal and Image Processing, Spring 2007
Course Directors: Dr. Julie Greenberg
HST582J/6.555J/16.456J
Biomedical
Signal
and
Image
Processing
Spring
2007
Chapter
8
 LINEAR
PREDICTION
c
±
Bertrand
Delgutte
1999
Introduction
Linear
prediction
is
a
widelyused
signal
processing
technique
in
which
the
current
value
of
a
discretetime
signal
is
approximated
by
a
ﬁnite
weighted
sum
of
its
past
values.
It
is
mathemat
ically
equivalent
to
the
techniques
of
autoregressive
spectral
estimation,
and
maximumentropy
estimation.
The
central
idea
behind
these
techniques
is
that
the
signal
is
modeled
as
the
response
of
an
allpole
(autoregressive)
ﬁlter
to
a
white
signal.
Spectral
estimation
is
then
equivalent
to
estimating
the
coeﬃcients
of
the
allpole
ﬁlter.
These
techniques
are
well
suited
to
signals
whose
spectra
show
sharp
peaks
such
as
the
formants
of
speech.
In
the
case
of
speech
signals,
linear
prediction
takes
a
special
signiﬁcance
in
the
context
of
the
sourceﬁlter
model
of
speech
production.
According
to
this
model,
speech
is
the
output
of
a
timevarying
ﬁlter
(representing
the
vocal
tract
resonances
and
radiation
characteristics)
ex
cited
by
either
a
voicing
source
or
a
noise
source
(Fig.
1a).
Under
certain
assumptions,
linear
prediction
can
separate
the
contributions
of
the
source
and
the
ﬁlter
to
the
speech
signal,
i.e.
it
can
deconvolve
the
source
signal
from
the
impulse
response
of
the
ﬁlter.
This
property
con
trasts
with
those
of
the
shorttime
Fourier
transform,
which
provides
a
spectral
representation
of
speech
in
which
e±ects
of
the
source
and
the
ﬁlter
are
scrambled,
and
which
is
heavily
dependent
on
the
choice
of
an
analysis
window.
The
deconvolution
property
of
linear
prediction
is
useful
in
biomedical
applications
because
the
source
and
the
ﬁlter
correspond
to
di±erent
anatomi
cal
structures,
and
are
therefore
a±ected
by
di±erent
clinical
conditions.
Linear
prediction
is
also
widely
used
in
telecommunication
engineering
and
automatic
speech
recognition
because
it
represents
speech
in
terms
of
a
small
number
of
parameters
that
contain
the
most
important
information
for
intelligibility.
8.1
Allpole
model
of
speech
8.1.1
From
the
source±lter
model
to
the
allpole
model
In
order
to
show
how
linear
prediction
can
separate
the
contributions
of
the
source
and
the
ﬁlter
to
speech,
we
need
to
simplify
somewhat
the
speechproduction
model
of
Fig.
1a
by
making
two
additional
assumptions:
(1)
that
the
ﬁlter
is
allpole
(purelyrecursive,
or
autoregressive)
and
(2)
that
the
source
is
”white”
in
the
sense
that
it
has
a
ﬂat
spectral
envelope.
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 Spring '07
 JulieGreenberg
 Image processing, Signal Processing, linear prediction, Bertrand Delgutte, sp eech

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