Forums

Estimate LPC's

Started by rahulparthasarthy May 17, 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 writing a C program for the above expression.

Regards,
Rahul Parthasarthy




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 >




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.