The Levinson recursion involves inverting the covariance matrix
toeplitz(r), and the first one is poorly conditioned. You can see this in
matlab by setting the first autocorrelation vector to r, and the second one
to r2.

You will find that cond(toeplitz(r)) = 9.3491e+004, and cond(toeplitz(r2))
= 3.0142e+003. The first condition value is much larger, which indicates
the accuracy of the results of a matrix inversion. 

>Why does the 10th order levinson durbin algorithm return these LP
>coefficients
>
>
>LPC
>
>                         1
>         -141.987085255646
>          379.380008989783
>         -652.562624856013
>          914.226857127382
>         -1069.00679555295
>          1068.49193530997
>         -912.915274765544
>          650.564278635448
>         -377.394102649473
>           140.21469138077
>
>for this autocorrelation sequence :
>
>                         1
>         0.954887218045113
>         0.892857142857143
>         0.887218045112782
>         0.892857142857143
>          0.87406015037594
>         0.862781954887218
>         0.868421052631579
>         0.862781954887218
>         0.849624060150376
>         0.847744360902256
>
>
>If I use this (similar) autocorrelation sequence
>
>
>                         1
>         0.955932203389831
>                       0.9
>         0.896610169491525
>         0.903389830508475
>         0.884745762711864
>         0.871186440677966
>         0.869491525423729
>         0.855932203389831
>         0.838983050847458
>         0.832203389830508
>
>I get these LP coefficients:
>
>                         1
>         -1.34686071095947
>          1.06567003975718
>         -0.75978856644957
>        0.0294126810016533
>         0.258696591668145
>        -0.319917626183194
>        0.0360131660377147
>         0.155615320440029
>        -0.201467558173645
>         0.101029788353466
>
>
>Normally, the LP coefficients are in the range from -12 to 12 ...but
>for certain autocorrelation sequences the numbers just blow
>up....What's the reason? How do you handle these special cases?
>
>

Rune Allnor wrote:

> On Mar 14, 9:47 pm, John McDermick <johnthedsp...@gmail.com> wrote:
> 
>>Why does the 10th order levinson durbin algorithm return these LP
>>coefficients
> 
> ....
> 
>>Normally, the LP coefficients are in the range from -12 to 12 ...but
>>for certain autocorrelation sequences the numbers just blow
>>up....What's the reason? How do you handle these special cases?
> 
> 
> Use some sort of order estimator.

In the audio applications, they usually apply some fudge factors to the 
ACF coefficients, decreasing ACF from lower to higher orders. This could 
be thought of as an addition of the colored noise to the signal, making 
LPC model dull and stable.

Vladimir Vassilevsky
DSP and Mixed Signal Design Consultant
http://www.abvolt.com

On Mar 14, 9:47&#4294967295;pm, John McDermick <johnthedsp...@gmail.com> wrote:
> Why does the 10th order levinson durbin algorithm return these LP
> coefficients
...
> Normally, the LP coefficients are in the range from -12 to 12 ...but
> for certain autocorrelation sequences the numbers just blow
> up....What's the reason? How do you handle these special cases?

Use some sort of order estimator.

Rune

Why does the 10th order levinson durbin algorithm return these LP
coefficients


LPC

                         1
         -141.987085255646
          379.380008989783
         -652.562624856013
          914.226857127382
         -1069.00679555295
          1068.49193530997
         -912.915274765544
          650.564278635448
         -377.394102649473
           140.21469138077

for this autocorrelation sequence :

                         1
         0.954887218045113
         0.892857142857143
         0.887218045112782
         0.892857142857143
          0.87406015037594
         0.862781954887218
         0.868421052631579
         0.862781954887218
         0.849624060150376
         0.847744360902256


If I use this (similar) autocorrelation sequence


                         1
         0.955932203389831
                       0.9
         0.896610169491525
         0.903389830508475
         0.884745762711864
         0.871186440677966
         0.869491525423729
         0.855932203389831
         0.838983050847458
         0.832203389830508

I get these LP coefficients:

                         1
         -1.34686071095947
          1.06567003975718
         -0.75978856644957
        0.0294126810016533
         0.258696591668145
        -0.319917626183194
        0.0360131660377147
         0.155615320440029
        -0.201467558173645
         0.101029788353466


Normally, the LP coefficients are in the range from -12 to 12 ...but
for certain autocorrelation sequences the numbers just blow
up....What's the reason? How do you handle these special cases?