Accessibility of zero-input limit cycles

The notion of accessibility, introduced by Claasen et al., has been very helpful in determining properties of zero-input limit cycles in digital filters. In this paper we show that accessibility places restrictions on the error sequences introduced at the quantizers. Both 2's complement rounding and truncation, with one and two quantizers, are investigated. These results provide a very simple method for determining whether a particular limit cycle is accessible. It is also shown that large limit cycles are likely to be accessible. For the case with two quantizers, the error sequence constraints are used to derive conditions on the amplitudes of accessible limit cycles. Finally, it is shown that only certain states of a filter can directly access a limit cycle.