Why can 'e' not be positive in levinson function?

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Ezz El-din Abdullah 2017-8-6

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编辑： Ezz El-din Abdullah 2017-8-6

I know that, theoretically, the error prediction comping out from the levinson algorithm should be positive and less than 1.

Why levinson() can not produce such an output matching to the theory?

Should I make some normalization or so?

Also, I would like to contact the technical support of MATLAB to ask about the algorithm itself. So can anyone tell me how I can find the technical support.

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John D'Errico 2017-8-6

编辑：John D'Errico 2017-8-6

If you want to contact technical support, why not just click on the "contact us" button, on the top right of your browser page here? Answers is not technical support. At least, not official tech support.

Ezz El-din Abdullah 2017-8-6

Thank you.

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Answer 1

Jan 2017-8-6

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/351730-why-can-e-not-be-positive-in-levinson-function#answer_276994

Finding the technical support is easy. Do you see the "Contact Us" link on the top right of this page?

What are your inputs? Which output do you get for e? Which Matlab version are you using? Do you use the same definition of e as Matlab's function?

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Jan 2017-8-6

在 MATLAB Online 中打开

Sorry, can you please post the original values of the inputs you use? I did not meant the definition of the function, but the mathematical definition. Note that all, the documentation explains is:

[a,e] = levinson(r,n) returns the prediction error, e, of order n.

So perhaps this e is not what you exactly expect as "error prediction". As soon as even the value does not match your definition, this seems to be sure.

Provide the input data, such that the forum can confirm the problem. Perhaps it is a damaged Matlab function on your computer only.
Provide the definition which let you assume, that e should by inside [0,1].

Ezz El-din Abdullah 2017-8-6

编辑：Ezz El-din Abdullah 2017-8-6

在 MATLAB Online 中打开

This is my test code:

%%Test Data
fs      = 200; 
fo      = 1;
phi     = 0;
ts      = 1/fs;
T       = 4;
t       = -T/2:ts:T/2-ts;
xt      = .7*(1 + cos(2*pi*fo*t - phi));
%%Auto-correlation 
order     = 2; 
[R,lags] = xcorr(xt,order);              % restrict the autocorr to be from -2 to 2
R        = ts/T * R;
[a,e] = levinson(R,order); % e = -0.0056

The definition of e is:

e_n = e_{n-1} * (1 - | Q |^2)

where Q is a reflection coefficient and it is less than or equal 1 and e is recursively computed and when n-1 = 0 e was equal the average power of the zero mean of the sample which is less than 1.

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