Almost period P sequences and the analysis of forced overflow oscillations in digital filters

We introduce here the new concept of "almost period sequences" and we show how this concept can be used to extend significantly our understanding of the behavior of digital filters when certain finite register length effects are taken into consideration. Concerning forced overflow oscillations in particular, we prove that even when the period of a digital filter\´s periodic input waveform is constrained to lie within an arbitrarily small interval of values, the digital filter is still susceptible to the occurrence of forced overflow oscillations.