Cascading Wiener-Hammerstein systems

In this paper we study the cascading of weakly nonlinear systems. It is shown that the best linear approximation of the cascaded system is given by the product of the best linear approximation to the first and second nonlinear system respectively. This approximation is valid in the frequency range where both coherences of the individual linear approximations are high. In case both cascaded systems are Wiener-Hammerstein, the coherence provides also insight into the distribution of the dynamics over both system.