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levinson
Levinson-Durbin recursion.
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
levinson produces is minimum phase.
a = levinson(r,n)
finds the coefficients of an nth-order autoregressive linear process which has r as its autocorrelation sequence. r is a real deterministic autocorrelation sequence (a vector), and n is the order of denominator polynomial a(z), that is, a = [1 a(2) ... a(n+1)]. The filter coefficients are ordered in descending powers of z:
levinson solves the symmetric Toeplitz system of linear equations:
where r = [R(1) ... R(n+1)] is the input autocorrelation vector. The algorithm requires O(n2) flops and is thus much more efficient than the MATLAB \ command for large n. However, the levinson function uses \ for low orders to give the fastest possible execution.