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?

# levinson durbin algorithm

Started by ●March 14, 2011

Reply by ●March 15, 20112011-03-15

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. Rune

Reply by ●March 15, 20112011-03-15

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

Reply by ●March 15, 20112011-03-15

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? > >