Nonlinear systems can be approximated by linear time-invariant (LTI) models in many ways. Here, LTI models that are optimal approximations in the meansquare error sense are analyzed. A necessary and sufficient condition on the input signal for the optimal LTI approximation of an arbitrary nonlinear finite impulse response (NFIR) system to be a linear finite impulse response (FIR) model is prese...

Model reduction and convex optimization are prevalent in science and engineering applications. In this thesis, convex optimization solution techniques to three different model reduction problems are studied. Parameterized reduced order modeling is important for rapid design and optimization of systems containing parameter dependent reducible sub-circuits such as interconnects and RF inductors. ...

This work considers behavioral modeling, parameter-reduction, and digital predistortion of radio frequency power amplifiers. Due to the use of modern digital modulation methods, contemporary power amplifiers are frequently subjected to signals characterized by considerable bandwidths and fast changing envelopes. As a result, traditional quasi-memoryless amplitude-to-amplitude (AM/AM) and amplit...

The paper addresses the problem of non-parametric estimation of the static characteristic in Wiener-Hammerstein (sandwich) system excited and disturbed by random processes. A new, kernel-like method is presented. The proposed estimate is consistent under small amount of a priori information. An IIR dynamics, non-invertible static non-linearity, and non-Gaussian excitations are admitted. The con...

Skeletal muscle force can be estimated using surface electromyographic (sEMG) signals. Usually, the sEMG location for the sensors is near the respective muscle motor unit points. Skeletal muscles generate a temporal and spatial distributed EMG signal, which causes cross talk between different sEMG signal sensors. In this paper, an array of three sEMG sensors is used to capture the information o...

The notion of frequency response functions has been generalized to nonlinear systems in several ways. However, a relation between different approaches has not yet been established. In this paper, frequency domain representations for nonlinear systems are uniquely connected. Specifically, by means of novel analytical results, the generalized frequency response function (GFRF) and the higher orde...

Wiener-Hammerstein systems consist of a linear dynamic system followed by a static nonlinearity, followed by another linear dynamic system. These models are difficult to identify due to the presence of two dynamic systems. Usually, a nonlinear estimation procedure is used to estimate the parameters of the different parts. This nonlinear estimation procedure needs good starting values to converg...

A Markov chain approach to identification of the Wiener, Hammerstein, and nonlinear ARX (NARX) systems is presented. The motivation of this approach comes from the fact that these classes of nonlinear systems are connected with Markov chains, and hence their asymptotical properties, such as ergodicity, stationarity, and invariant probability distribution, can be derived from the corresponding c...