Related papers: Best Linear Approximation of Nonlinear Continuous-…
The Best Linear Approximation (BLA) framework has already proven to be a valuable tool to analyze nonlinear systems and to start the nonlinear modeling process. The existing BLA framework is limited to systems with additive (colored) noise…
A Distortion Contribution Analysis (DCA) obtains the distortion at the output of an analog electronic circuit as a sum of distortion contributions of its sub-circuits. Similar to a noise analysis, a DCA helps a designer to pinpoint the…
We consider the problem of nonlinear filtering of one-dimensional diffusions from noisy measurements. The filter is said to lose lock if the estimation error exits a prescribed region. In the case of phase estimation this region is one…
In this study, we consider the experimentally-obtained, periodically-forced response of a nonlinear structure in the presence of process noise. Control-based continuation is used to measure both the stable and unstable periodic solutions…
The Frequency Response Functions (FRFs) are the most widely used functions to characterise the dynamic behaviour of structures. The natural frequencies and damping behaviour can be easily and quickly detected from a Bode diagram. The modal…
We discuss the problem how to determine the quality of a nonlinear system with respect to a measurement task. Due to amplification, filtering, quantization and internal noise sources physical measurement equipment in general exhibits a…
Nonlinearity in many systems is heavily dependent on component variation and environmental factors such as temperature. This is often overcome by keeping signals close enough to the device's operating point that it appears approximately…
The problem of optimal linear estimation of a linear functional depending on the unknown values of periodically correlated stochastic process from observations of the process with additive noise is considered. Formulas for calculating the…
Presented is a new algorithm for estimating the frequency of a single-tone noisy signal using linear least squares (LLS). Frequency estimation is a nonlinear problem, and typically, methods such as Nonlinear Least Squares (NLS) (batch) or a…
In this paper, an approximation recursive formula of the mean-square error lower bound for the discrete-time nonlinear filtering problem when noises of dynamic systems are temporally correlated is derived based on the Van Trees (posterior)…
Nanomechanical resonators are used in building ultra-sensitive mass and force sensors. In a widely used resonator based sensing paradigm, each modal resonance frequency is tracked with a phase-locked loop (PLL) based system. There is great…
We derive the ultimate bounds on the performance of nonlinear measurement schemes in the presence of noise. In particular, we investigate the precision of the second-order estimation scheme in the presence of the two most detrimental types…
Many modern engineering structures exhibit nonlinear vibration. Characterizing such vibrations efficiently is critical to optimizing designs for reliability and performance. For linear systems, steady-state vibration occurs only at the…
A novel method for noise reduction in the setting of curve time series with error contamination is proposed, based on extending the framework of functional principal component analysis (FPCA). We employ the underlying, finite-dimensional…
We have developed a new methodology and a time-domain software package for the estimation of the oscillation frequency and the phase noise spectrum of non-linear noisy microwave circuits based on the direct integration of the system of…
This paper deals with the phase noise affecting communication systems, where local oscillators are employed to obtain reference signals for carrier and timing synchronizations. The most common discrete-time phase noise channel model is…
The problem of measuring the best linear approximation of a nonlinear system by means of multilevel excitation sequences is analyzed. A comparison between different types of sequences applied at the input of Wiener systems is provided by…
We revisit the problem of non-parametric closed-loop identification in frequency domain; we give a brief survey of the literature and provide a small noise analysis of the direct, indirect, and joint input-output methods when two…
We propose solution of the problem of the mean square optimal estimation of linear functionals which depend on the unobserved values of a continuous time stochastic process with periodically correlated increments based on observations of…
Improvement in time resolution sometimes introduces short-range random noises into temporal data sequences. These noises affect the results of power-spectrum analyses and the Detrended Fluctuation Analysis (DFA). The DFA is one of useful…