The New Wavelet-like Allan Variance Based on the Atomic Function

A novel wavelet-like variance similar to the Allan variance, based on the infinitely differentiable atomic function is introduced. This variance is intended for phase and frequency instability analysis of signals arising in systems requiring high-quality time and frequency sources. Unlike the conventional Allan variance and its known generalizations and modifications, the proposed variance is appropriate for analyzing signals in presence of arbitrary power-law fluctuations due to outstanding time-domain and spectral properties of the atomic function. Theoretical analysis of model signals with known power-law spectra is performed, demonstrating the advantages of the novel mathematical tool for frequency instability investigation.