Estimating the number of components of a multicomponent nonstationary signal using the short-term time-frequency Rényi entropy

This article proposes a method for estimating the local number of signals components using the short term Rényi entropy of signals in the time-frequency plane. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).The time-frequency Rényi entropy provides a measure of complexity of a nonstationary multicomponent signal in the time-frequency plane. When the complexity of a signal corresponds to the number of its components, then this information is measured as the Rényi entropy of the time-frequency distribution (TFD) of the signal. This article presents a solution to the problem of detecting the number of components that are present in short-time interval of the signal TFD, using the short-term Rényi entropy. The method is automatic and it does not require a prior information about the signal. The algorithm is applied on both synthetic and real data, using a quadratic separable kernel TFD. The results confirm that the short-term Rényi entropy can be an effective tool for estimating the local number of components present in the signal. The key aspect of selecting a suitable TFD is also discussed

An improved method for nonstationary signals components extraction based on the ICI rule

This paper presents an automatic adaptive method to localize and extract signal components from a noisy multicomponent signal TFD. (Additional details can be found in the comprehensive book on Time-Frequency Signal Analysis and Processing (see http://www.elsevier.com/locate/isbn/0080443354). In addition, the most recent upgrade of the original software package that calculates Time-Frequency Distributions and Instantaneous Frequency estimators can be downloaded from the web site: www.time-frequency.net. This was the first software developed in the field, and it was first released publicly in 1987 at the 1st ISSPA conference held in Brisbane, Australia, and then continuously updated).This paper proposes an improved adaptive algorithm for components localization and extraction from a noisy multicomponent signal time-frequency distribution (TFD). The algorithm, based on the intersection of confidence intervals (ICI) rule, does not require any a priori knowledge of signal components and their mixture. Its efficiency is significantly enhanced by using high resolution and reduced cross-terms TFDs. The obtained results are compared for different signal-to-noise ratios (SNRs) and various time and lag window types used in the modified B-distribution (MBD) calculation, proving the method to be a valuable tool in noisy multicomponent signals components extraction in the time-frequency (TF) domain

Meadowdale High School Student with Disabilities Finds Job in UD Cafeteria; UD Assistant Geology Professor Plots City\u27s Glacial Deposits on High-Tech Map

Feature leads for the media: The University of Dayton and Dayton Public Schools have teamed up to place a Meadowdale High School student with multiple disabilities in a job with Kennedy Union Food Service; UD geology faculty member J. Michael Clinch is using a computer to create Dayton and Montgomery County\u27s first extensive and only automated inventory of glacial and post-glacial deposits on a U.S. Geological Survey base map

Segmentation of Non-Stationary Signals with Applications

Non-stationary signals are partitioned into near stationary segments using a modified Appel and Brandt algorithms. The modification requires two spectral distance measures to be used to produce an algorithm which is insensitive to changes in signal energy level which are irrelevant in this application. Performance on real and simulated data is presented. Segmentation has been used to provide an estimator of the evolution spectrum and an application to a noisy communication signal is presented

IF Estimation for Multicomponent Signals Using Image Processing Techniques in the Time-Frequency Domain

This paper presents a method for estimating the instantaneous frequency (IF) of multicomponent signals. The technique involves, firstly, the transformation of the one dimensional signal to the two dimensional time-frequency domain using a reduced interference quadratic time-frequency distribution. IF estimation of signal components is then achieved by implementing two image processing steps: local peak detection of the time--frequency (TF) representation followed by an image processing technique called component linking. The proposed IF estimator is tested on noisy synthetic monocomponent and multicomponent signals exhibiting linear and nonlinear laws. For low signal to noise ratio (SNR) environments, a time-frequency peak filtering preprocessing step is used for signal enhancement. Application of the IF estimation scheme to real signals is illustrated with newborn EEG signals. Finally, to illustrate the potential use of the proposed IF estimation method in classifying signals based on their TF components' IFs, a classification method using least squares data-fitting is proposed and illustrated on synthetic and real signals

A Unified Approach to the STFT, TFDs and Instantaneous Frequency

Spectral analysis of time varying signals is traditionally performed with the short time Fourier transformation (STFT). In the last few years, many authors have advocated the use of time frequency distributions for this task. This paper has 2 main aims. The first is to reformulate Cohen-class of time frequency representations (TFRs) into discrete-time, discrete-frequency, computer-implemented form. The second aim is to show how, in this form, many of the properties of the continuous-time, continuous-frequency formulation are either lost or altered. Intuitions applicable in the continuous-time case examined here. The properties of the discrete variable formulation examined are the presence and form of cross-terms, instantaneous frequency (IF) estimation and relations between Cohen's class TFRs. We define a parameterized class of distributions which is a blending between the STFT and wigner ville distribution (WVD). The two main conclusions to be drawn are that all TFRs of Cohen's class implementable in the form (which includes all commonly used TFRs) posses cross terms and that IF estimation using periodic moments of these TFRs is purposeless, since simpler methods obtain the same results

Identifying phase synchronization clusters in spatially extended dynamical systems

We investigate two recently proposed multivariate time series analysis techniques that aim at detecting phase synchronization clusters in spatially extended, nonstationary systems with regard to field applications. The starting point of both techniques is a matrix whose entries are the mean phase coherence values measured between pairs of time series. The first method is a mean field approach which allows to define the strength of participation of a subsystem in a single synchronization cluster. The second method is based on an eigenvalue decomposition from which a participation index is derived that characterizes the degree of involvement of a subsystem within multiple synchronization clusters. Simulating multiple clusters within a lattice of coupled Lorenz oscillators we explore the limitations and pitfalls of both methods and demonstrate (a) that the mean field approach is relatively robust even in configurations where the single cluster assumption is not entirely fulfilled, and (b) that the eigenvalue decomposition approach correctly identifies the simulated clusters even for low coupling strengths. Using the eigenvalue decomposition approach we studied spatiotemporal synchronization clusters in long-lasting multichannel EEG recordings from epilepsy patients and obtained results that fully confirm findings from well established neurophysiological examination techniques. Multivariate time series analysis methods such as synchronization cluster analysis that account for nonlinearities in the data are expected to provide complementary information which allows to gain deeper insights into the collective dynamics of spatially extended complex systems

Data driven optimal filtering for phase and frequency of noisy oscillations: application to vortex flowmetering

A new method for extracting the phase of oscillations from noisy time series is proposed. To obtain the phase, the signal is filtered in such a way that the filter output has minimal relative variation in the amplitude (MIRVA) over all filters with complex-valued impulse response. The argument of the filter output yields the phase. Implementation of the algorithm and interpretation of the result are discussed. We argue that the phase obtained by the proposed method has a low susceptibility to measurement noise and a low rate of artificial phase slips. The method is applied for the detection and classification of mode locking in vortex flowmeters. A novel measure for the strength of mode locking is proposed.Comment: 12 pages, 10 figure

Tomographic analysis of reflectometry data II: the phase derivative

A tomographic technique has been used in the past to decompose complex signals in its components. The technique is based on spectral decomposition and projection on the eigenvectors of a family of unitary operators. Here this technique is also shown to be appropriate to obtain the instantaneous phase derivative of the signal components. The method is illustrated on simulated data and on data obtained from plasma reflectometry experiments in the Tore Supra.Comment: 25 pages, Latex, 17 figure

A tomographic analysis of reflectometry data I: Component factorization

Many signals in Nature, technology and experiment have a multi-component structure. By spectral decomposition and projection on the eigenvectors of a family of unitary operators, a robust method is developed to decompose a signals in its components. Different signal traits may be emphasized by different choices of the unitary family. The method is illustrated in simulated data and on data obtained from plasma reflectometry experiments in the tore Supra.Comment: 27 pages Latex, 17 figure