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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 writing a C program for the above expression. Regards, Rahul Parthasarthy |
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Estimate LPC's
Started by ●May 17, 2004
Reply by ●May 18, 20042004-05-18
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r u interested in finding y[n] from x[n] for any given y & x? if so, then u need an adaptive filter. use a simple LMS like this a=randn(L,1) for n=L:N inp=x(i-L+1:i); y1(n)=a'*inp; e(n)=y(n)-y1(n); a=a+eeta*e(n)*inp; end hope this helps ganesan phd student www.ufl.edu Quoting rahulparthasarthy <>: > 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 writing 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. > > _____________________________________ > About this discussion group: > > To Join: > > To Post: > > To Leave: > > Archives: http://www.yahoogroups.com/group/speechcoding > > Other DSP-Related Groups: http://www.dsprelated.com > > Yahoo! Groups Links > |
Reply by ●May 18, 20042004-05-18
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Hello Rahul, As Arijit and I have discussed in this e-group some days ago, your case will result in normal equations Ra = -r where vector r is not constrained by matrix R. In fact, vector r is the cross-correlation between x and y. While Durbin's solution does not apply any more, Levinson's solution still does. Hope this will help. Regards, Miguel -- Miguel Arjona Ramez rahulparthasarthy wrote: > > 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 writing 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. |
