Impact of Euro-Markets on the United States Balance of Payments

\u97Identication of time-invariant linear dynamic systems is a mature subject. In this contribution we focus on the interplay between methods that use time and frequency domain data, respectively. The frequency domain data could be either input/output Fourier transforms or frequency functions. We explain how these different kinds of data types are used to fit models, and how closely related the methods are. Of special interest is how transients (initial conditions and deviations from periodic signals) are handled. Direct estimation of time-continuous models is also discussed, as well as software aspects

Defining Fundamental Frequency for Almost Harmonic Signals

In this work, we consider the modeling of signals that are almost, but not quite, harmonic, i.e., composed of sinusoids whose frequencies are close to being integer multiples of a common frequency. Typically, in applications, such signals are treated as perfectly harmonic, allowing for the estimation of their fundamental frequency, despite the signals not actually being periodic. Herein, we provide three different definitions of a concept of fundamental frequency for such inharmonic signals and study the implications of the different choices for modeling and estimation. We show that one of the definitions corresponds to a misspecified modeling scenario, and provides a theoretical benchmark for analyzing the behavior of estimators derived under a perfectly harmonic assumption. The second definition stems from optimal mass transport theory and yields a robust and easily interpretable concept of fundamental frequency based on the signals' spectral properties. The third definition interprets the inharmonic signal as an observation of a randomly perturbed harmonic signal. This allows for computing a hybrid information theoretical bound on estimation performance, as well as for finding an estimator attaining the bound. The theoretical findings are illustrated using numerical examples.Comment: Accepted for publication in IEEE Transactions on Signal Processin

Modelling and filtering almost periodic signals by time-varying fourier series with application to near-infrared spectroscopy

We propose a new approach to modelling almost periodic signals and to model-based estimation of such signals from noisy observations. The signal model is based on Fourier series where both the coefficients and the fundamental frequency can continuously change over time. This signal model can be represented by a factor graph which we use to derive message passing algorithms to estimate the time-dependent model parameters from the observed samples

Quasi-periodic spatiotemporal models of brain activation in single-trial MEG experiments

Magneto-encephalography (MEG) is an imaging technique which measures neuronal activity in the brain. Even when a subject is in a resting state, MEG data show characteristic spatial and temporal patterns, resulting from electrical current at specific locations in the brain. The key pattern of interest is a ‘dipole’, consisting of two adjacent regions of high and low activation which oscillate over time in an out-of-phase manner. Standard approaches are based on averages over large numbers of trials in order to reduce noise. In contrast, this article addresses the issue of dipole modelling for single trial data, as this is of interest in application areas. There is also clear evidence that the frequency of this oscillation in single trials generally changes over time and so exhibits quasi-periodic rather than periodic behaviour. A framework for the modelling of dipoles is proposed through estimation of a spatiotemporal smooth function constructed as a parametric function of space and a smooth function of time. Quasi-periodic behaviour is expressed in phase functions which are allowed to evolve smoothly over time. The model is fitted in two stages. First, the spatial location of the dipole is identified and the smooth signals characterizing the amplitude functions for each separate pole are estimated. Second, the phase and frequency of the amplitude signals are estimated as smooth functions. The model is applied to data from a real MEG experiment focusing on motor and visual brain processes. In contrast to existing standard approaches, the model allows the variability across trials and subjects to be identified. The nature of this variability is informative about the resting state of the brain

Frequency Estimation Using Time-Frequency Based Methods

Any periodic signal can be decomposed into a sum of oscillating functions. Traditionally, cosine and sine segments have been used to represent a single period of the periodic signal (Fourier Series). In more general cases, each of these functions can be represented by a set of spectral parameters such as its amplitude, frequency, phase, and the variability of its instantaneous spectral components. The accuracy of these parameters depends on several processing variables such as resolution, noise level, and bias of the algorithm used. This thesis presents some background of existing frequency estimation techniques and proposes a new technique for estimating the instantaneous frequency of signals using short sinusoid-like basis functions. Furthermore, it also shows that the proposed algorithm can be implemented in a popular embedded DSPmicroprocessor for practical use. This algorithm can also be implemented using more complex features on more resourceful processing processors in order to improve estimation accurac

Combined Invariant Subspace \& Frequency-Domain Subspace Method for Identification of Discrete-Time MIMO Linear Systems

Recently, a novel system identification method based on invariant subspace theory is introduced, aiming to address the identification problem of continuous-time (CT) linear time-invariant (LTI) systems by combining time-domain and frequency-domain methods. Subsequently, the combined Invariant-Subspace and Subspace Identification Method (cISSIM) is introduced, enabling direct estimation of CT LTI systems in state-space forms. It produces consistent estimation that is robust in an error-in-variable and slow-sampling conditions, while no pre-filtering operation of the input-output signals is needed. This paper presents the discrete-cISSIM, which extends cISSIM to discrete-time (DT) systems and offers the following improvements: 1) the capability to utilize arbitrary discrete periodic excitations while cISSIM uses multi-sine signals; 2) a faster estimation with reduced computational complexity is proposed; 3) the covariance estimation problem can be addressed concurrently with the system parameter estimation. An implementation of discrete-cISSIM by MATLAB has also been provided.Comment: algorithm implemented via MATLAB: https://github.com/wyqy/dcissi

Mitigation of Side-Effect Modulation in Optical OFDM VLC Systems

Side-effect modulation (SEM) has the potential to be a significant source of interference in future visible light communication (VLC) systems. SEM is a variation in the intensity of the light emitted by a luminaire and is usually a side-effect caused by the power supply used to drive the luminaires. For LED luminaires powered by a switched mode power supply, the SEM can be at much higher frequencies than that emitted by conventional incandescent or fluorescent lighting. It has been shown that the SEM caused by commercially available LED luminaires is often periodic and of low power. In this paper, we investigate the impact of typical forms of SEM on the performance of optical OFDM VLC systems; both ACO-OFDM and DCO-OFDM are considered. Our results show that even low levels of SEM power can significantly degrade the bit-error-rate performance. To solve this problem, an SEM mitigation scheme is described. The mitigation scheme is decision-directed and is based on estimating and subtracting the fundamental component of the SEM from the received signal. We describe two forms of the algorithm; one uses blind estimation while the other uses pilot-assisted estimation based on a training sequence. Decision errors, resulting in decision noise, limit the performance of the blind estimator even when estimation is based on very long signals. However, the pilot system can achieve more accurate estimations, thus better performance. Results are first presented for typical SEM waveforms for the case where the fundamental frequency of the SEM is known. The algorithms are then extended to include a frequency estimation step and the mitigation algorithm is shown also to be effective in this case

The Relationship Between Instantaneous Frequency and Time-Frequency Representations

This paper describes a procedure for the time-frequency analysis of signals based on Time-Frequency Distribution (TFD) and Instantaneous Frequency (IF) estimation. First we use a suitable TFD to determine the number of signal components. Then if the signal is monocomponent , the IF law cam be estimated directly. For multi component signals, two-dimensional windowing in the time frequency (t-f) domain (a form of time varying filtering) is used to isolate each component; IF estimation is then applied to the individual components. The periodic first moment of a TFD is used to estimate the IF. A suitable definition of the periodic first moment is proposed, and the relationship of these estimators to other based on the central finite differences of the phase of the analytic signal is given. A TFD such as the Winger-Ville Distribution may be used to represent both IF and amplitude variations in the individual signal components at each stage of the analysis