Variance outputs
===================

The :func:`~spectrum.burg.arburg` function returns the AR parameters but also an estimation of the variance.

The following example plots the estimated variance (using arburg function) versus the true variance for different values of variance. In other words,  we plot how accurately the variance can be estimated.


.. plot::
    :width: 80%
    :include-source:

    from pylab import *
    import scipy.signal
    from spectrum import *

    # Define AR filter coefficients
    a = [1, -2.2137, 2.9403, -2.1697, 0.9606];

    # for different variance, 
    true_variance = linspace(0.1, 1, 20)
    estimated_variance = []
    for tv in true_variance:
        x = scipy.signal.lfilter([1], a, tv**0.5 * randn(1,256))
        AR, v, k = arburg(x[0], 4) # we estimate the AR parameter and variance
        estimated_variance.append(v)

    plot(true_variance, estimated_variance, 'o')
    xlabel('true variance')
    ylabel('estimated variance')
    plot([0,0],[1,1])
    axis([0,1,0,1])