On chaos of digital filters in the real world

Numerical simulations are presented showing that over certain parameter ranges, the asymptotic behavior of a real-world digital filter having a wordlength of only 16 b is virtually indistinguishable from that of an infinite wordlength digital filter. It is suggested that for all practical purposes, a finite-state machine can behave in a chaotic way if its wordlength is sufficiently large. It is concluded that the chaotic nature of a real digital filter may be hidden because of short wordlengths, but the chaotic behavior must be considered in a real digital filter when the wordlength exceeds 16 b