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.TH lev 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
lev - Yule-Walker equations (Levinson's algorithm)
.SH CALLING SEQUENCE
.nf
[ar,sigma2,rc]=lev(r)
.fi
.SH PARAMETERS
.TP 12
r
: correlation coefficients
.TP
ar
: auto-Regressive model parameters
.TP
sigma2
: scale constant
.TP
rc
: reflection coefficients
.SH DESCRIPTION
resolve the Yule-Walker equations
.IG
.nf
|R(0) R(1) ... R(N-1)|| ar(1) | |sigma2|
|R(1) R(0) ... R(N-2)|| ar(2) | | 0 |
| : : ... : || : |=| 0 |
| : : ... : || : | | 0 |
|R(N-1) R(N-2) ... R(0) ||ar(N-1)| | 0 |
where
R(i)=r(i-1)
.fi
.FI
.LA $$ \left( \matrix{ R_0 & R_1 & \ldots & R_{N-1} \cr
.LA R_1 & R_0 & \ldots & R_{N-2} \cr
.LA \vdots & \vdots & \ldots & \vdots \cr
.LA R_{N-1} & R_{N-2} & \ldots & R_{0} \cr
.LA } \right) \vector{ ar_1 \cr ar_2 \cr \vdots \cr
.LA ar_{N-1}}
.LA = \vector{ \sigma_2 \cr 0 \cr \vdots \cr 0} $$
.LA where $R_i=r(i-1)$.
using Levinson's algorithm.
.SH AUTHOR
C. B.
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