Statistical Properties of a Certain Periodic Binary Process
Arthur Wouk · Technometrics · 1966
The magnitude S of a certain signal is to be measured in the presence of a noise N. In order to improve the accuracy of the measurement, it will be repeated and essentially averaged by summing all the measurements. Consider a measuring device which at each stage of measurement adds or subtracm exactly one bit at the low end of a counter. Assume that the signal S together with an additive noise N is essentially restricted to some interval say −1 ≤ S ≤ 1. The interval [−1, 1] is divided by a mesh of reference values A sequencing arrangement allows the comparison of S + N with each ri in some pattern which is periodic of period p. If S + N > ri , add +1 while if S + N < ri add −1 to the counter (which is initially set at zero). Assume that if S + N = ri , the assignment of ±1 is unbiased, and that each ri is used exactly one time in each period. We describe the statistics of the contents of the counter at some time after the start of measurements.