FIR Lattice Filter Reflection Coefficients in Terms of Direct Coefficients?

Hi Folks,

Maybe I'm dense, but I don't see a way (recursive or otherwise)
in P&M to go from the FIR direct form coefficients, the "b[n]" in

  y[i] = \sum_{n=0}^{N-1} x[i-n] * b[n],

to FIR lattice filter reflection coeffients K_m. Does anyone know how
and/or have a reference?
-- 
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124

Do you have Matlab?  It has conversion routines for various filter topologies.

"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxpy8ht9tp3.fsf@usrts005.corpusers.net...
> Hi Folks,
>
> Maybe I'm dense, but I don't see a way (recursive or otherwise)
> in P&M to go from the FIR direct form coefficients, the "b[n]" in
>
>   y[i] = \sum_{n=0}^{N-1} x[i-n] * b[n],
>
> to FIR lattice filter reflection coeffients K_m. Does anyone know how
> and/or have a reference?
> -- 
> Randy Yates
> Sony Ericsson Mobile Communications
> Research Triangle Park, NC, USA
> randy.yates@sonyericsson.com, 919-472-1124

"Jon Harris" <goldentully@hotmail.com> writes:

> Do you have Matlab?  It has conversion routines for various filter topologies.

Yes, I have Matlab, but I have to know how to do this manually on a test.

--Randy

> 
> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
> news:xxpy8ht9tp3.fsf@usrts005.corpusers.net...
> > Hi Folks,
> >
> > Maybe I'm dense, but I don't see a way (recursive or otherwise)
> > in P&M to go from the FIR direct form coefficients, the "b[n]" in
> >
> >   y[i] = \sum_{n=0}^{N-1} x[i-n] * b[n],
> >
> > to FIR lattice filter reflection coeffients K_m. Does anyone know how
> > and/or have a reference?
> > -- 
> > Randy Yates
> > Sony Ericsson Mobile Communications
> > Research Triangle Park, NC, USA
> > randy.yates@sonyericsson.com, 919-472-1124
> 
> 

-- 
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
randy.yates@sonyericsson.com, 919-472-1124

Ah, a homework question!  :-)

You could try looking at the .m file for the Matlab method to see if that gives
you any clues.  I have a feeling it might be really general and hard to
understand though, but maybe not.

"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxpu0sh9rsp.fsf@usrts005.corpusers.net...
> "Jon Harris" <goldentully@hotmail.com> writes:
>
> > Do you have Matlab?  It has conversion routines for various filter
topologies.
>
> Yes, I have Matlab, but I have to know how to do this manually on a test.
>
> --Randy
>
> >
> > "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
> > news:xxpy8ht9tp3.fsf@usrts005.corpusers.net...
> > > Hi Folks,
> > >
> > > Maybe I'm dense, but I don't see a way (recursive or otherwise)
> > > in P&M to go from the FIR direct form coefficients, the "b[n]" in
> > >
> > >   y[i] = \sum_{n=0}^{N-1} x[i-n] * b[n],
> > >
> > > to FIR lattice filter reflection coeffients K_m. Does anyone know how
> > > and/or have a reference?
> > > -- 
> > > Randy Yates
> > > Sony Ericsson Mobile Communications
> > > Research Triangle Park, NC, USA
> > > randy.yates@sonyericsson.com, 919-472-1124

Hello Randy,
You probably are too tired from studing too much, so you missed it. In O&S's
Discrete-Time Signal Processing, an example is on page 320. Ex. 6.7 shows
converting an ordinary FIR to a Lattice form. The recursion formula is given
by (6.56c)

IHTH,
Clay



"Randy Yates" <randy.yates@sonyericsson.com> wrote in message
news:xxpy8ht9tp3.fsf@usrts005.corpusers.net...
> Hi Folks,
>
> Maybe I'm dense, but I don't see a way (recursive or otherwise)
> in P&M to go from the FIR direct form coefficients, the "b[n]" in
>
>   y[i] = \sum_{n=0}^{N-1} x[i-n] * b[n],
>
> to FIR lattice filter reflection coeffients K_m. Does anyone know how
> and/or have a reference?
> -- 
> Randy Yates
> Sony Ericsson Mobile Communications
> Research Triangle Park, NC, USA
> randy.yates@sonyericsson.com, 919-472-1124

Randy Yates wrote:

> Hi Folks,
> 
> Maybe I'm dense, but I don't see a way (recursive or otherwise)
> in P&M to go from the FIR direct form coefficients, the "b[n]" in
> 
>   y[i] = \sum_{n=0}^{N-1} x[i-n] * b[n],
> 
> to FIR lattice filter reflection coeffients K_m. Does anyone know how
> and/or have a reference?

Doesn't section 11.2.2, backward prediction, cover it?


Bob
-- 

"Things should be described as simply as possible, but no 
simpler."

                                              A. Einstein

"Clay Turner" <physics@bellsouth.net> wrote in message news:<NbEfd.41754$qH3.39398@bignews6.bellsouth.net>...
> Hello Randy,
> You probably are too tired from studing too much, so you missed it. In O&S's
> Discrete-Time Signal Processing, an example is on page 320. Ex. 6.7 shows
> converting an ordinary FIR to a Lattice form. The recursion formula is given
> by (6.56c)
> 
> IHTH,
> Clay

Eh... what edition of the book do you refer to? I just wanted to see 
what you're discussing and looked up in my 2nd edition (apparently 
from 1999, although that's not very clear, but with Buck as co-author), 
and can't find anything there that appears to be relevant to this thread?

Rune

> "Randy Yates" <randy.yates@sonyericsson.com> wrote in message
> news:xxpy8ht9tp3.fsf@usrts005.corpusers.net...
> > Hi Folks,
> >
> > Maybe I'm dense, but I don't see a way (recursive or otherwise)
> > in P&M to go from the FIR direct form coefficients, the "b[n]" in
> >
> >   y[i] = \sum_{n=0}^{N-1} x[i-n] * b[n],
> >
> > to FIR lattice filter reflection coeffients K_m. Does anyone know how
> > and/or have a reference?
> > -- 
> > Randy Yates
> > Sony Ericsson Mobile Communications
> > Research Triangle Park, NC, USA
> > randy.yates@sonyericsson.com, 919-472-1124

Randy Yates <randy.yates@sonyericsson.com> wrote in message news:<xxpy8ht9tp3.fsf@usrts005.corpusers.net>...
> Hi Folks,
> 
> Maybe I'm dense, but I don't see a way (recursive or otherwise)
> in P&M to go from the FIR direct form coefficients, the "b[n]" in
> 
>   y[i] = \sum_{n=0}^{N-1} x[i-n] * b[n],
> 
> to FIR lattice filter reflection coeffients K_m. Does anyone know how
> and/or have a reference?

Does the section on p 518 (containing example 7.2.3) help?
Equations 7.2.55-56 seem to be useful. Remember to start the 
recursion with the *last* coefficient in the direct-form 
implementation, though...

Rune

"Rune Allnor" <allnor@tele.ntnu.no> wrote in message
news:f56893ae.0410270359.69471832@posting.google.com...
> "Clay Turner" <physics@bellsouth.net> wrote in message
news:<NbEfd.41754$qH3.39398@bignews6.bellsouth.net>...
> > Hello Randy,
> > You probably are too tired from studing too much, so you missed it. In
O&S's
> > Discrete-Time Signal Processing, an example is on page 320. Ex. 6.7
shows
> > converting an ordinary FIR to a Lattice form. The recursion formula is
given
> > by (6.56c)
> >
> > IHTH,
> > Clay
>
> Eh... what edition of the book do you refer to? I just wanted to see
> what you're discussing and looked up in my 2nd edition (apparently
> from 1999, although that's not very clear, but with Buck as co-author),
> and can't find anything there that appears to be relevant to this thread?
>
> Rune

Hello Rune,
I'm referring to the 1st edition of Discrete Time Signal Processing (c)
1989. Some people used to call it the "2nd edition" although it is renamed
and so officially it is a new book. The original O&S is Digital Signal
Processing (c) 1975. I have both of these versions, yet I haven't gotten the
version with Buck as co-author. The original text doesn't have any
formulations for Lattice filters. It will be kind of sad if the third
version has cut some of this out. The 2nd version cut out the chapter on
Homomorphic Signal Processing. I guess the publisher only allows a certain
size for the book, so when the authors add something, something else must
go!

Later,
Clay

"Clay Turner" <physics@bellsouth.net> writes:

> Hello Randy,
> You probably are too tired from studing too much, so you missed it. In O&S's
> Discrete-Time Signal Processing, an example is on page 320. Ex. 6.7 shows
> converting an ordinary FIR to a Lattice form. The recursion formula is given
> by (6.56c)
>
> IHTH,

Yup, thanks Clay.

--Randy


-- 
%  Randy Yates                  % "With time with what you've learned, 
%% Fuquay-Varina, NC            %  they'll kiss the ground you walk 
%%% 919-577-9882                %  upon."
%%%% <yates@ieee.org>           % '21st Century Man', *Time*, ELO
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