ORBIT-PERIODS IN SECOND-ORDER FINITE-PRECISION DIGITAL FILTERS WITH OVERFLOW

Abstract

The effect of n-bit precision on the orbit-periods of second-order lossless overflowing digital filters is discussed. It is observed that there are of the order of 2n orbits with periods O(2n), whereas in a random finite-state machine with the same number (2n)2 of states and with an invertible next-state function there are a few large orbits with periods O((2n)2). This behavior persists when the coefficient multiplication is replaced by a random mapping. This "randomized" model is readily understood and so provides a rough theory of the orbit-periods.