title: Allan variance and fractal Brownian motion
abstract: Noise filtering is the subject of a voluminous literature in radio engineering. The methods of filtering require knowledge of the frequency response, which is usually unknown. D.W. Allan (see Proc. IEEE, vol.54, no.2, p.221-30, 1966; IEEE Trans. Instr. Measur., vol.IM-36, p.646-54, 1987) proposed a simple method of determining the interval between equally accurate observations which does without this information. In this method, the variances of the increments of noise and signal are equal, so that, in observations with a greater step, the variations caused by noise are smaller than those caused by the signal. This method is the standard accepted by the USA metrology community. The present paper is devoted to a statistical analysis of the Allan method and acquisition of additional information
keyphrases: Allan variance fractal Brownian motion noise filtering radio engineering frequency response USA metrology community statistical analysis white noise