document: Allan variance and fractal Brownian motion 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 -LRB- see Proc . IEEE , vol .54 , no. 2 , p.221-30 , 1966 ; IEEE Trans . Instr . Measur. , vol.IM-36 , p.646-54 , 1987 -RRB- 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
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