The science of modelling the behaviour of natural phenomena and physical systems has grown significantly in importance in the last century. It helps us to understand and predict natural phenomena or improve and control all types of industrial processes. There are basically two approaches to system modelling: a model can be derived from physical knowledge of the system or by systematically testing it and estimating the model structure and parameters based on the test data. The method of system testing has gained importance due to the increasing complexity of modern industrial systems and processes. It also serves as a verification tool to the physical model. It has led to a rapid advance of a particular discipline within science generally referred to as system identification. This thesis deals with a frequency domain approach to identifying a particular class of nonlinear systems which can be modelled by the Volterra series. The methodology is based on the application of specially designed multisine test signals which allow second and third order terms of the Volterra series, so-called Volterra kernels, to be measured directly and the structure of the nonlinear system to be identified. In the first part of this thesis an introduction is given to system identification in the frequency domain and the analysis of a particular class of nonlinear systems using the Volterra series. Particular attention is given to the design of multisine signals and the development of a comprehensive software tool to aid with the identification task. The second part examines Volterra kernels and the application of block-oriented models to Volterra systems. A method is proposed for identifying the structure of such models based on Volterra kernels and in particular for the de-composition of a cascade structure into its linear dynamic components. The contributions made in this work include the development of a software tool for system identification, the measurement and representation of frequency domain Volterra kernels, as well as the classification and decomposition of block-oriented models by applying specially designed multisine signals.

This thesis deals with a simulation of analogue audio effects using the nonlinear models that replace the analogue nonlinear devices in discrete domain. The thesis describes Volterra system model and simplified Volterra system model that can be realized in two ways, either Wiener model, or Hammerstein model. The method for the analysis and modeling of audio and acoustic nonlinear systems is presented in this thesis. This method allows through knowledge of the input swept-sine signal and the response of the analogue nonlinear system to the input signal to determine the coefficients of the discrete nonlinear system. This allows simulating the analogue nonlinear system in discrete domain. The method was first tested and then used successfully for simulation of the analogue nonlinear system in discrete domain. Concretely, it was simulated a musical guitar effect of the type of distortion. Last part of this thesis is devoted a description of VST technology and an implementation of VST plug-in module, which realizations Hammerstein model.