Normalized histogram of the state variable of first-order digital filters with two’s complement arithmetic

Abstract

In this letter, the normalized histogram of the state variable of first-order digital filters with two’s complement arithmetic is investigated. When the pole of the digital filter is between 1 and 2, it is found that the possibility of occurrence of the state variable in certain region is close to zero no matter what the initial condition is. Some analytic results are given to account for this phenomenon