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Syntax
a = levinson(r,p)
Description
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 thatlevinson produces is minimum phase.
a = levinson(r,p)
finds the coefficients of an pth-order autoregressive linear process which has r as its autocorrelation sequence. r is a real or complex deterministic autocorrelation sequence (a vector), and p is the order of denominator polynomial A(z); that is, a = [1 a(2) ... a(p+1)]. The filter coefficients are ordered in descending powers of z:
Algorithm
levinson solves the symmetric Toeplitz system of linear equations.
r = [r(1) ... r(p+1)] is the input autocorrelation vector, and r(i)* denotes the complex conjugate of r(i). The algorithm requires O(p2) flops and is thus much more efficient than the MATLAB \ command for large p. However, the levinson function uses \ for low orders to provide the fastest possible execution.
See Also
lpc |
Linear prediction coefficients. |
prony |
Prony's method for time domain IIR filter design. |
rlevinson |
Reverse Levinson-Durbin recursion. |
stmcb |
Linear model using Steiglitz-McBride iteration. |
References
[1] Ljung, L. System Identification: Theory for the User. Englewood Cliffs, NJ: Prentice Hall, 1987. Pgs. 278-280.