Signal Transformations by Nonlinearity as The Foundation for Identification Procedures

Abstract

Nonlinear effects in a network include the generation of 'new' spectral components: distortion products, notably harmonics and intermodulation products. In the method of polynomial correlation specific use is made of these distortion products. A polynomial correlation function is the cross-correlation function of the output signal and a distorted version of the input signal. The method is most useful for specific classes of non-linear systems.For systems consisting of a first linear filter, followed by a memoryless nonlinear element and a second linear filter, application of Hermite polynomial correlation technique leads to surprisingly simple results. A short derivation of the main theorem of polynomial correlation is presented. In practical application the method is found to have many pitfalls, some of these are of an obscure nature. Practical problems concerning finite sample size, aliasing and the use of non-ideal Gaussian noise are discussed. The effects of these problems are shown via the results of simulation examples.