Systems consisting of linear dynamic and memoryless nonlinear subsyste
ms are identified. The paper deals with systems in which the nonlinear
element is followed by a linear element, as well as systems in which
the subsystems are connected in parallel. The goal of the identificati
on is to recover the nonlinearity from noisy input-output observations
of the whole system; signals interconnecting the elements are not mea
sured. Observed values of the input signal are rearranged in increasin
g order, and coefficients for the expansion of the nonlinearity in tri
gonometric series are estimated from the new sequence of observations
obtained in this way Two algorithms are presented, and their mean inte
grated square error is examined. Conditions for pointwise convergence
are also established. For the nonlinearity satisfying the Lipschitz co
ndition, the error converges to zero. The rate of convergence derived
for differentiable nonlinear characteristics is insensitive to the rou
ghness of the probability density of the input signal. Results of nume
rical simulation are also presented.