avar 0.0.4

Allan variance tools

Allan Variance Tools

Array of Windows

avar.windows(K, density=64)

This will create an array M of integer window sizes. The averaging period tau would equal M*T, where T is the sampling period. The density is the target number of window sizes in the array per decade. Obviously, in the first decade it is not possible to have more than 9 window sizes: 1 through 9.

Signal Allan Variance

avar.variance(y, M)

To get the actual Allan variance of a signal y, use this function. You must supply the array of window sizes M for which to calculate the Allan variance values. This function can take for y either a one-dimensional array or a two-dimensional array in which each row will be treated as a data set.

Ideal Allan Variance

avar.ideal(tau, vc, taub=None)

Given a set of five component noise variances vc, you can calculate what the ideal Allan variances would be over an array of averaging periods tau. The five component noises are quantization, white, flicker, walk, and ramp. Any noise components you wish not to include, set their corresponding variances to zero. If you wish to treat flicker noise as an idealized, flat Allan variance over averaging period, leave the first-order, Gauss-Markov (FOGM) time constant, taub, as None. If you wish to treat the flicker noise as a FOGM noise, set the time constant to some non-zero value.

Fitting to Signal Allan Variance

avar.fit(tau, va, taub=None, mask=None, tol=0.007)

Given the Allan variance curve of some signal, va, at various averaging periods tau, you can get the best fit using the five component noises. As with the ideal function, if taub is left undefined, the flicker noise will be treated as the idealized, flat Allan variance over averaging period. Otherwise, the flicker noise will be treated as a first-order, Gauss-Markov noise. Although this function will automatically attempt to determine if certain component noises are even at play based on the tolerance value tol, you can directly control which component noises you wish to exclude with the mask array. For each element of mask that is False the corresponding component noise will be excluded.

Noise Generation

avar.noise(vc, K, T, taub=None)

Given a five-element array of component noise variances vc, you can create an artificially-generated noise signal of length K and sampling period T. Each element of vc corresponds to one of the five component noise types: quantization, white, flicker, walk, and ramp. As with the ideal function, if taub is left undefined, the flicker noise will be treated as the idealized, flat Allan variance over averaging period. Otherwise, the flicker noise will be treated as a first-order, Gauss-Markov noise.