Forums

Estimate LPC's

Started by rahulparthasarthy May 18, 2004
Hello,

I am trying to compute a solution using the least- square- error
principle to an overdetermined system of equations.

The equation is as below:

Error = summation (y[n] summation (ai x[n-i] ) )... in 'ai'
term `i' is subscript

where `n' ranges from 1 to 300 and `i' ranges from 1 to 18. The
outside summation is for `n' (1,2,3,4,299,300) whereas the inside
summation is for 'i' (1,2,3,418)

I am interested in calculating `ai ` ( i is subscript) where 'ai'
represents Linear Prediction Coefficients. I could have used the
Levinson-Durbin algorithm but in this case, two different signals are
in consideration, namely, y[n] and x[n], and hence
the `autocorrelation' method cannot be used. I have y[n] and x[n]
available but not able to evaluate that expression.

I would be obliged if anybody could help me in solving/evaluating
the above equation so that I can find ai's (LP coefficients). Is it
possible to solve using Maple, Matlab, Mathematica etc? I am
interested in developing a C program for the above expression.

Regards,
Rahul Parthasarthy




I suggest you look at any adaptive processing text. It will have this
exact problem and its closed-form solution.

Maurice Givens On Mon, 17 May 2004 23:14:57 -0000 "rahulparthasarthy"
<> writes:
> Hello,
>
> I am trying to compute a solution using the least- square- error
> principle to an overdetermined system of equations.
>
> The equation is as below:
>
> Error = summation (y[n] summation (ai x[n-i] ) )... in 'ai'
> term `i' is subscript
>
> where `n' ranges from 1 to 300 and `i' ranges from 1 to 18. The
> outside summation is for `n' (1,2,3,4,299,300) whereas the inside
>
> summation is for 'i' (1,2,3,418)
>
> I am interested in calculating `ai ` ( i is subscript) where 'ai'
> represents Linear Prediction Coefficients. I could have used the
> Levinson-Durbin algorithm but in this case, two different signals
> are
> in consideration, namely, y[n] and x[n], and hence
> the `autocorrelation' method cannot be used. I have y[n] and x[n]
> available but not able to evaluate that expression.
>
> I would be obliged if anybody could help me in solving/evaluating
> the above equation so that I can find ai's (LP coefficients). Is it
>
> possible to solve using Maple, Matlab, Mathematica etc? I am
> interested in developing a C program for the above expression.
>
> Regards,
> Rahul Parthasarthy > ------------------------ Yahoo! Groups Sponsor
>
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A solution to an overdermined linear system can be found
by either SVD or QR decomposition methods. They are stored
somewhere on the net. E.g. CLAPACK on http://netlib.org.

We have a commercial solution for C6000 and TS. Please
contact me if you need more information.

Rgds,
Andrew

--
Andrew V. Nesterov ()
Optimized TMS320C6000 DSP Software
http://microprocessing.iwarp.com

> Date: Mon, 17 May 2004 23:14:57 -0000
> From: "rahulparthasarthy" <>
> Subject: Estimate LPC's
>
> Hello,
>
> I am trying to compute a solution using the least- square- error
> principle to an overdetermined system of equations.
>
> The equation is as below:
>
> Error = summation (y[n] ? summation (ai x[n-i] ) )... in 'ai'
> term `i' is subscript
>
> where `n' ranges from 1 to 300 and `i' ranges from 1 to 18. The
> outside summation is for `n' (1,2,3,4,?299,300) whereas the inside
> summation is for 'i' (1,2,3,4?18)
>
> I am interested in calculating `ai ` ( i is subscript) where 'ai'
> represents Linear Prediction Coefficients. I could have used the
> Levinson-Durbin algorithm but in this case, two different signals are
> in consideration, namely, y[n] and x[n], and hence
> the `autocorrelation' method cannot be used. I have y[n] and x[n]
> available but not able to evaluate that expression.
>
> I would be obliged if anybody could help me in solving/evaluating
> the above equation so that I can find ai's (LP coefficients). Is it
> possible to solve using Maple, Matlab, Mathematica etc? I am
> interested in developing a C program for the above expression.
>
> Regards,
> Rahul Parthasarthy





Hello,
 
Thank you for your help and support.
 
I found the right solution to this problem in one Signal Processing book.
This problem is solved in book entitled 'Optimal and Adaptive Signal Processing' by Peter M. Clarkson (in Chapter 2). They have derived an expression to solve these kind of eaquations (Ax=B). I have developed C program to  solve Ax=B, but I haven't used QR Decomposition, I have used simple matrix inversion technique.
 
Once again, thank you for for you help and support.
 
Regards,
Rahul Parthasarthy.

Andrew Nesterov <a...@softhome.net> wrote:

A solution to an overdermined linear system can be found
by either SVD or QR decomposition methods. They are stored
somewhere on the net. E.g. CLAPACK on http://netlib.org.

We have a commercial solution for C6000 and TS. Please
contact me if you need more information.

Rgds,
Andrew

--
Andrew V. Nesterov (a...@softhome.net)
Optimized TMS320C6000 DSP Software
http://microprocessing.iwarp.com

> Date: Mon, 17 May 2004 23:14:57 -0000
> From: "rahulparthasarthy" <r...@yahoo.com>
> Subject: Estimate LPC's
>
> Hello,
>
> I am trying to compute a solution using the least- square- error
> principle to an overdetermined system of equations.
>
> The equation is as below:
>
> Error = summation (y[n] ? summation (ai  x[n-i] ) )... in  'ai'
> term `i' is subscript
>
> where `n' ranges from 1 to 300 and  `i' ranges from 1 to 18. The
> outside summation is for `n' (1,2,3,4,?299,300)  whereas the inside
> summation is for 'i' (1,2,3,4?18)
>
> I am interested in calculating `ai ` ( i  is subscript) where 'ai'
> represents Linear Prediction Coefficients.  I could have used the
> Levinson-Durbin algorithm but in this case, two different signals are
> in consideration, namely, y[n] and x[n], and hence
> the `autocorrelation' method cannot be used. I have y[n] and x[n]
> available but not able to evaluate that expression.
>
> I would be obliged if anybody could help me in solving/evaluating
> the above equation so that I can find ai's (LP coefficients). Is it
> possible to solve using Maple, Matlab, Mathematica etc? I am
> interested in developing a C program for the above expression.
>
> Regards,
> Rahul Parthasarthy


_____________________________________
Note: If you do a simple "reply" with your email client, only the author of this message will receive your answer.  You need to do a "reply all" if you want your answer to be distributed to the entire group.

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I thought you needed to solve an overdermined system, for which
an inverse matrix does not exist.

If you has reduced it to a square matrix, you can use faster methods
to solve it, but even that you do not need to compute an inverse
matrix to obtain a solution to a linear system.

Rgds,

Andrew

> Date: Thu, 20 May 2004 09:53:14 -0700 (PDT)
> From: Rahul Parthasarthy <>
> Subject: Re: Re: Estimate LPC's
>
> Hello,
>
> Thank you for your help and support.
>
> I found the right solution to this problem in one Signal Processing book.
> This problem is solved in book entitled 'Optimal and Adaptive Signal
> Processing' by Peter M. Clarkson (in Chapter 2). They have derived an
> expression to solve these kind of eaquations (Ax=B). I have developed C
> program to solve Ax=B, but I haven't used QR Decomposition, I have used
> simple matrix inversion technique.
>
> Once again, thank you for for you help and support.
>
> Regards,
> Rahul Parthasarthy.
>
> Andrew Nesterov <> wrote:
>
> A solution to an overdermined linear system can be found
> by either SVD or QR decomposition methods. They are stored
> somewhere on the net. E.g. CLAPACK on http://netlib.org.
>
> We have a commercial solution for C6000 and TS. Please
> contact me if you need more information.
>
> Rgds,
> Andrew
>
> --
> Andrew V. Nesterov ()
> Optimized TMS320C6000 DSP Software
> http://microprocessing.iwarp.com
>
> > Date: Mon, 17 May 2004 23:14:57 -0000
> > From: "rahulparthasarthy" <>
> > Subject: Estimate LPC's
> >
> > Hello,
> >
> > I am trying to compute a solution using the least- square- error
> > principle to an overdetermined system of equations.
> >
> > The equation is as below:
> >
> > Error = summation (y[n] ? summation (ai x[n-i] ) )... in 'ai'
> > term `i' is subscript
> >
> > where `n' ranges from 1 to 300 and `i' ranges from 1 to 18. The
> > outside summation is for `n' (1,2,3,4,?299,300) whereas the inside
> > summation is for 'i' (1,2,3,4?18)
> >
> > I am interested in calculating `ai ` ( i is subscript) where 'ai'
> > represents Linear Prediction Coefficients. I could have used the
> > Levinson-Durbin algorithm but in this case, two different signals are
> > in consideration, namely, y[n] and x[n], and hence
> > the `autocorrelation' method cannot be used. I have y[n] and x[n]
> > available but not able to evaluate that expression.
> >
> > I would be obliged if anybody could help me in solving/evaluating
> > the above equation so that I can find ai's (LP coefficients). Is it
> > possible to solve using Maple, Matlab, Mathematica etc? I am
> > interested in developing a C program for the above expression.
> >
> > Regards,
> > Rahul Parthasarthy
> >
> >
>