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[ni] ) )... 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 LevinsonDurbin 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 

Estimate LPC's
Started by ●May 18, 2004
Reply by ●May 19, 200420040519
I suggest you look at any adaptive processing text. It will have this exact problem and its closedform 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[ni] ) )... 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 > LevinsonDurbin 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 > > _____________________________________ > 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. > > _____________________________________ > About this discussion group: > > To Join: > > To Post: > > To Leave: > > Archives: http://www.yahoogroups.com/group/echocancel > > Other DSPRelated Groups: http://www.dsprelated.com > > Yahoo! Groups Links > > ________________________________________________________________ The best thing to hit the Internet in years  Juno SpeedBand! Surf the Web up to FIVE TIMES FASTER! Only $14.95/ month  visit www.juno.com to sign up today! 
Reply by ●May 19, 200420040519
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[ni] ) )... 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 > LevinsonDurbin 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 

Reply by ●May 20, 200420040520
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:

Reply by ●May 22, 200420040522
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[ni] ) )... 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 > > LevinsonDurbin 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 > > > > > 