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# levinson() - Signal Processing

### Syntax

### Example

### Output / Return Value

### Limitations

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### Reference

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) finds the coefficients of a length(r)-1 order autoregressive linear process which has r as its autocorrelation sequence. r is a real or complex deterministic autocorrelation sequence. If r is a matrix, levinson finds the coefficients for each column of r and returns them in the rows of a. n=length(r)-1 is the default order of the denominator polynomial A(z); that is, a = [1 a(2) ... a(n+1)]. The filter coefficients are ordered in descending powers of z–1.H(z)=1A(z)=11+a(2)z−1+⋯+a(n+1)z−na = levinson(r,n) returns the coefficients for an autoregressive model of order n.[a,e] = levinson(r,n) returns the prediction error, e, of order n. [a,e,k] = levinson(r,n) returns the reflection coefficients k as a column vector of length n. Note k is computed internally while computing the a coefficients, so returning k simultaneously is more efficient than converting a to k with tf2latc.

a = levinson(r)a = levinson(r,n)[a,e] = levinson(r,n)[a,e,k] = levinson(r,n)

Autoregressive Process CoefficientsOpen This Example Estimate the coefficients of an autoregressive process given by a = [1 0.1 -0.8]; Generate a realization of the process by filtering white noise of variance 0.4.rng('default') v = 0.4; w = sqrt(v)*randn(15000,1); x = filter(1,a,w); Estimate the correlation function. Discard the correlation values at negative lags. Use the Levinson-Durbin recursion to estimate the model coefficients.[r,lg] = xcorr(x,'biased'); r(lg<0) = []; ar = levinson(r,numel(a)-1) ar = 1.0000 0.0957 -0.8026