MATLAB: Does the LEVINSON function not require the auto-correlation value R(0) in Signal Processing Toolbox 6.9 (R2008a)

Signal Processing Toolbox

The "Algorithm" section of the documentation for the LEVINSON function says:

 levinson solves the symmetric Toeplitz system of linear equations ...
 where r = [r(1)  ... r(n+1)] is the input auto-correlation vector

Clearly, the zeroth lag correlation value should be a part of the calculation, but it does not appear in the input vector "r".

Best Answer

This change has been incorporated into the documentation in Release 2009b (R2009b). For previous releases, read below for any additional information:

The documentation is using MATLAB-style indexing for the input auto-correlation vector "r", as "r(1)" actually refers to the first element of the auto-correlation vector "r", which is the zeroth lag correlation value.

This is further confirmed by typing

help levinson
 at the MATLAB prompt, as the following text is displayed:
 Input R is typically a vector of auto-correlation coefficients with lag 0 as the first element.

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MATLAB: Levinson Algorithm

Have you tried levinson in MATLAB?

help levinson

BTW I'm not quite sure if I understand your Rxx. Are you referring to a covariance matrix or is this just a sequence?

MATLAB: Scalar Levinson Algorithm and Autocorrelation in MATLAB

I was able to solve the indices problem and correctly solve the levinson recursion equations. Posting just in case someone needs this in the future!

% Initialization
P = zeros(1,3);
alpha = zeros(1,3);
a(1,1) = -autocorr(2)/autocorr(1);
P(1) = autocorr(1);
P(2) = autocorr(1) - ((autocorr(2)^2)/autocorr(1));
% Start Algorithm
for N = 1:numlag-2
    sum = 0;
    for j = 1:N
        sum = sum + a(N,j)*autocorr(N+2-j);
    end
    alpha(N,1) = autocorr(N+2) + sum;
for i = 1:N
    a(N+1,i) = a(N,i) - (alpha(N)/P(N+1))*a(N,N+1-i);
end
    a(N+1,i) = a(N,i) - (alpha(N)/P(N+1))*a(N,N+1-i);
    a(N+1,N+1) = - alpha(N)/P(N+1);
    P(N+2) = P(N+1) - (alpha(N))^2/P(N+1);
    
% Tolerance Checks    
    zerochecker = abs(P(2) - P(1));
    if zerochecker < 0.5 
        N = 0;
        break
    end
    check = abs(abs(P(N+2)) - abs(P(N+1)));
    if  check < 1
        break
    end
end

As a BONUS I am posting my autocorrelation sequence below:

function [autocorr] = corr(numlag,dataD,n)
% autocorrelation sequence
for ii = 1:numlag
    lag = ii - 1;
        for iii = 1:n-lag
            seq1(iii,ii) = dataD(iii).* dataD(iii+lag);         
            numer = sum(seq1);
        end
        autocorr_unrounded = round(numer,2)';
end
autocorr = autocorr_unrounded/n;
end

Best Answer

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MATLAB: Scalar Levinson Algorithm and Autocorrelation in MATLAB

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