The Fig. presents the block diagram of an ideal second order digital filter.
The differential discret equation that described the system is given by:
Now, we replace the ideal operators (adder and multiplactor) by real operaters that are presents in Digital Signal Processors (DSP) when realising recursive filters. The associated non-linear function is the modulo function, wich represents the effect of the overflow that occurs in digital implementation. The non-linear system is then described by a non-linear discret state equations system :
Te = 1 Tfin = 1e4*Te Nbit = 31 a=0.5 b=-1 ci=0.675 Intmax = 2^(Nbit-1); ci1=-int(ci*Intmax) ci2=int(ci*Intmax)