a = levinson(r,n)
The Levinson-Durbin recursion is an algorithm for finding an
all-pole IIR filter with a prescribed deterministic
autocorrelation sequence. It has applications in filter design, coding,
and spectral estimation. The filter that
is minimum phase.
the coefficients of a
length(r)-1 order autoregressive
linear process which has
r as its autocorrelation
r is a real or complex deterministic
autocorrelation sequence. If
r is a matrix,
the coefficients for each column of
r and returns
them in the rows of
the default order of the denominator polynomial A(z);
a = [1 a(2) ... a(n+1)]. The filter coefficients
are ordered in descending powers of z–1.
a = levinson(r,n) returns the coefficients
for an autoregressive model of order n.
[a,e] returns the prediction
error, e, of order n.
[a,e,k] returns the reflection
k as a column vector of length
levinson solves the symmetric Toeplitz system
of linear equations
r = [r(1) ... r(n+1)
the input autocorrelation vector, and r(i)* denotes
the complex conjugate of r(i).
r is typically a vector of autocorrelation
coefficients where lag 0 is the first element r(1).
The algorithm requires O(n2)
flops and is thus much more efficient than the MATLAB®
n. However, the
\ for low orders to provide the fastest possible
 Ljung, L., System Identification: Theory for the User, Prentice-Hall, 1987, pp. 278-280.