On wavelet variance

Frequency stability of an atomic clock can be characterized by wavelet variance. Wavelet variance puts a limit on the influence of nonlinear and non-stationary processes. The character of wavelet variance is analyzed by using Fractal Brownian Motion function as an example of atomic clock signal. As in the cases of Allan variance and Hadamard variance, we can choose a suitable basis function. It is proved that Allan variance is a special case of wavelet variance at Haar basis. Hadamard variance is a special case of wavelet variance where the scale is much large than 1. It is concluded that frequency stability of atomic clocks is characterized by wavelet variance