Nonparametric Spectral Analysis Research Articles

Determining the Dynamic Characteristics of a Multi-Story RC Building Located in Chile: A Comparison of the Results between the Nonparametric Spectral Analysis Method and the Parametric Stochastic Subspace Identification Method

Estimating the dynamic characteristics of instrumented built structures from seismic vibration data collected from built civil structures is essential input information for structural model updating and assessing the health of structures. This study focuses on the earthquake acceleration time histories obtained from several events recorded during its construction phase by accelerometers placed throughout an office building located in Viña del Mar (Chile) to determine its modal features. To this end, the data obtained were analyzed to compare the building’s dynamic properties obtained with two different modal identification techniques. MATLAB programs were developed to implement both methods. The stochastic subspace identification technique for linear systems developed by van Overschee and de Moor was used to study the dynamic properties of the building. In contrast, the nonparametric method employed herein uses correlations and spectral analysis based on the Welch transform in the frequency domain. The investigation demonstrated that both methods identify similar frequencies and that the obtained translational mode shapes exhibit good agreement. Furthermore, the identified frequencies are congruent with the design frequencies.

Power Spectral Density Background Estimate and Signal Detection via the Multitaper Method

AbstractWe present a new spectral analysis method for the identification of periodic signals in geophysical time series. We evaluate the power spectral density with the adaptive multitaper method, a nonparametric spectral analysis technique suitable for time series characterized by colored power spectral density. Our method provides a maximum likelihood estimation of the power spectral density background according to four different models. It includes the option for the models to be fitted on four smoothed versions of the power spectral density when there is a need to reduce the influence of power enhancements due to periodic signals. We use a statistical criterion to select the best background representation among the different smoothing + model pairs. Then, we define the confidence thresholds to identify the power spectral density enhancements related to the occurrence of periodic fluctuations (γ test). We combine the results with those obtained with the multitaper harmonic F test, an additional complex‐valued regression analysis from which it is possible to estimate the amplitude and phase of the signals. We demonstrate the algorithm on Monte Carlo simulations of synthetic time series and a case study of magnetospheric field fluctuations directly driven by periodic density structures in the solar wind. The method is robust and flexible. Our procedure is freely available as a stand‐alone IDL code at https://zenodo.org/record/3703168. The modular structure of our methodology allows the introduction of new smoothing methods and models to cover additional types of time series. The flexibility and extensibility of the technique makes it broadly suitable to any discipline.

Note on nonparametric spectral analysis of wideband spectrum with missing data via sample-and-hold interpolation and deconvolution

In [1] a procedure for bias-free estimation of the autocorrelation function is introduced for equidistantly sampled data with randomly occurring samples being invalid. The method incorporates sample-and-hold interpolation of the missing data points. The occurring dynamic error of the primary estimate of the correlation function is treated by a deconvolution procedure with two parameters c0 and c1 with c0+2c1=1, which are the on-diagonal and the aside-diagonal parameters of a specific correction matrix (at all lag times except zero). The parameters c0 and c1 were obtained as a function of the probability α of a sample to be valid by numerical simulation. However, explicit expressions for the parameters c0(α)=1−2α+2α2 and c1(α)=1α−1α2 can be derived, which might improve the usability of the deconvolution procedure in [1].

State Space Oscillator Models for Neural Data Analysis.

Neural oscillations reflect the coordinated activity of neuronal populations across a wide range of temporal and spatial scales, and are thought to play a significant role in mediating many aspects of brain function, including atten- tion, cognition, sensory processing, and consciousness. Brain oscillations are typically analyzed using frequency domain methods such as nonparametric spectral analysis, or time domain methods based on linear bandpass filtering. A typical analysis might seek to estimate the power within an oscillation sitting within a particular frequency band. A common approach to this problem is to estimate the signal power within that band, in frequency domain using the power spectrum, or in time domain by estimating the power or variance in a bandpass filtered signal. A major conceptual flaw in this approach is that neural systems, like many physiological or physical systems, have inherent broad-band 1/P' dynamics, whether or not an oscillation is present. Calculating power-in-band, or power in a bandpass filtered signal, can therefore be misleading, since such calculations do not distinguish between broadband power within the band of interest, and true underlying oscillations. In this paper, we present an approach for analyzing neural oscillations using a combination of linear oscillatory models. We estimate the parameters of these models using an expectation maximization (EM) algorithm, and employ AIC to select the appropriate model and identify the oscillations present in the data. We demonstrate the application of this method to univariate electroencephalogram (EEG) data recorded at quiet rest and during propofol-induced unconsciousness.

Nonparametric spectral analysis of heart rate variability through penalized sum of squares

Researchers in a variety of biomedical fields have utilized frequency domain properties of heart rate variability (HRV), or the elapsed time between consecutive heart beats. HRV is measured from the electrocardiograph signal through the interbeat interval series. Popular approaches for estimating power spectra from these interval data apply common spectral analysis methods that are designed for the analysis of evenly sampled time series. The application of these methods to the interbeat interval series, which is indexed over an uneven time grid, requires a bias-inducing transformation. The goal of this article is to explore the use of penalized sum of squares for nonparametric estimation of the spectrum of HRV directly from the interbeat intervals. A novel cross-validation procedure is introduced for smoothing parameter selection. Empirical properties of the proposed estimation procedure are explored and compared with popular methods in a simulation study. The proposed method is used in an analysis of data from an insomnia study, which seeks to illuminate the association between the power spectrum of HRV during different periods of sleep with response to behavioral therapy.

Nonparametric spectral analysis of wideband spectrum with missing data via sample-and-hold interpolation and deconvolution

Spectral estimation of data sequences with randomly missing samples is considered in this paper. A nonparametric missing-data method is proposed based on interpolation followed by a deconvolution procedure. Sample-and-hold interpolation is considered here. The method is based on the analytic expression of the autocorrelation function of the interpolated data as a linear function of the autocorrelation function of the data to be estimated. Bias and standard deviation of both autocorrelation function and power spectral density are detailed for simulated data based on Monte Carlo analysis. The method is also compared with a fuzzy slotting technique with local normalization and weighting algorithm. Based on the results of these simulations, it is concluded that the performance of the proposed method is better than those of the slotting technique.

High accuracy peak location and amplitude spectral estimation via tuning APES method

In this paper, we introduce a new approach to the method of non-parametric adaptive spectral analysis by using the Amplitude and Phase Estimation (APES) method, and taking into account the small sample errors of the sample covariance matrix. This approach is referred to as Adaptive Tuning Amplitude and Phase Estimation method (ATAPES). The main advantage of the ATAPES algorithm is its elimination of biased estimation exists with APES method, which is a biased peak location and corresponding problem of the biased amplitude estimation. The ATAPES method provides more accurate peak location and amplitude estimation with higher resolution than APES method.

Critical analysis of autoregressive and fast Fourier transform markers of cardiovascular variability in rats and humans

The autonomic nervous system plays an important role in physiological and pathological conditions, and has been extensively evaluated by parametric and non-parametric spectral analysis. To compare the results obtained with fast Fourier transform (FFT) and the autoregressive (AR) method, we performed a comprehensive comparative study using data from humans and rats during pharmacological blockade (in rats), a postural test (in humans), and in the hypertensive state (in both humans and rats). Although postural hypotension in humans induced an increase in normalized low-frequency (LFnu) of systolic blood pressure, the increase in the ratio was detected only by AR. In rats, AR and FFT analysis did not agree for LFnu and high frequency (HFnu) under basal conditions and after vagal blockade. The increase in the LF/HF ratio of the pulse interval, induced by methylatropine, was detected only by FFT. In hypertensive patients, changes in LF and HF for systolic blood pressure were observed only by AR; FFT was able to detect the reduction in both blood pressure variance and total power. In hypertensive rats, AR presented different values of variance and total power for systolic blood pressure. Moreover, AR and FFT presented discordant results for LF, LFnu, HF, LF/HF ratio, and total power for pulse interval. We provide evidence for disagreement in 23% of the indices of blood pressure and heart rate variability in humans and 67% discordance in rats when these variables are evaluated by AR and FFT under physiological and pathological conditions. The overall disagreement between AR and FFT in this study was 43%.

Nonparametric spectral analysis with applications to seizure characterization using EEG time series

Understanding the seizure initiation process and its propagation pattern(s) is a critical task in epilepsy research. Characteristics of the pre-seizure electroencephalograms (EEGs) such as oscillating powers and high-frequency activities are believed to be indicative of the seizure onset and spread patterns. In this article, we analyze epileptic EEG time series using nonparametric spectral estimation methods to extract information on seizure-specific power and characteristic frequency [or frequency band(s)]. Because the EEGs may become nonstationary before seizure events, we develop methods for both stationary and local stationary processes. Based on penalized Whittle likelihood, we propose a direct generalized maximum likelihood (GML) and generalized approximate cross-validation (GACV) methods to estimate smoothing parameters in both smoothing spline spectrum estimation of a stationary process and smoothing spline ANOVA time-varying spectrum estimation of a locally stationary process. We also propose permutation methods to test if a locally stationary process is stationary. Extensive simulations indicate that the proposed direct methods, especially the direct GML, are stable and perform better than other existing methods. We apply the proposed methods to the intracranial electroencephalograms (IEEGs) of an epileptic patient to gain insights into the seizure generation process.

Time–frequency analysis of click-evoked otoacoustic emissions by means of a minimum variance spectral estimation-based method

This paper proposes a new minimum variance spectral estimation (MVSE)-based time–frequency analysis (TFA) technique for click-evoked otoacoustic emissions (CEOAEs). The MVSE is a popular spectrum analysis method which can yield a high frequency resolution compared to other nonparametric spectral analysis procedures. The conventional MVSE is extended to a TFA method by windowing the observation data to obtain a time–frequency representation for the signal under study. Inspired by the adaptive window selection process in wavelet transform and based on the time–frequency characteristics of CEOAEs, the window size of the windowed MVSE (WMVSE) is given a small value at high frequencies and a large value at low frequencies. The adaptive window size selection yields the proposed frequency-dependent WMVSE (FDWMVSE). The FDWMVSE method integrates the advantages of the adaptive window selection in wavelet transform with the fine frequency resolution of MVSE. Experimental results show that the FDWMVSE can achieve satisfactory time–frequency resolution and reveal meaningful time–frequency features when applied to synthesized and real CEOAEs.

Statistical Signal Characterization of Spectral Analysis of Heart Rate Variability for Screening of Patients with Obstructive Sleep Apnea

A new screening technique for obstructive sleep apnea (OSA) is implemented. This technique is based on finding the statistical signal characterization (SSC) parameters of the spectrum of pre-processed R-R-interval (RRI) data. A single classification factor (CR) is selected to classify between patients with obstructive sleep apnea and normal controls. Both nonparametric spectral analysis techniques (with Welch method as an example) and parametric techniques (with Burg method as an example) are used to estimate the power spectral density. The data tested in this work are drawn from MIT database. Both trial and test (challenge) groups of data are used. Each of these two groups contains 20 OSA and 10 normal records. The trial data is used to set the threshold value of the classification factor, which is then used in identifying the challenge data. The total accuracy of the screening is about 93% and 90% using Burg and Welch algorithms respectively.

Support vector machines framework for linear signal processing

This paper presents a support vector machines (SVM) framework to deal with linear signal processing (LSP) problems. The approach relies on three basic steps for model building: (1) identifying the suitable base of the Hilbert signal space in the model, (2) using a robust cost function, and (3) minimizing a constrained, regularized functional by means of the method of Lagrange multipliers. Recently, autoregressive moving average (ARMA) system identification and non-parametric spectral analysis have been formulated under this framework. The generalized, yet simple, formulation of SVM LSP problems is particularized here for three different issues: parametric spectral estimation, stability of Infinite Impulse Response filters using the gamma structure, and complex ARMA models for communication applications. The good performance shown on these different domains suggests that other signal processing problems can be stated from this SVM framework.

Ventricular Fibrillation Median Frequency May Not Be Useful for Monitoring During Cardiac Arrest Treated with Endothelin-1 or Epinephrine

In this study, we evaluated whether median fibrillation frequency (MF) and mean fibrillation amplitude (AMP) reflect coronary perfusion pressure (CoPP) and predict successful defibrillation. MF, AMP, and CoPP were measured during prolonged ventricular fibrillation (VF) cardiac arrest and resuscitation in pigs. After 5 min of VF, cardiopulmonary resuscitation was started. At 10 min, the pigs received randomly a single dose of endothelin-1 50 mug (n = 7), 100 mug (n = 7), or 200 mug (n = 5), or repeated doses of epinephrine 0.04 mg/kg (n = 6), or saline (n = 6) every 3 min. At 25 min, the pigs were defibrillated to achieve restoration of spontaneous circulation (ROSC). In a nonparametric spectral analysis of the individual MF versus CoPP and AMP versus CoPP curves, we found no link between the different curves in different animals or therapies. No difference was found in MF in pigs with ROSC (n = 8) compared with animals not achieving ROSC (n = 23) immediately before defibrillation (P = 0.85). Our data suggest that, in prolonged VF cardiac arrest, MF and AMP might not be useful tools to reflect myocardial perfusion.

Nonparametric spectral analysis with missing data via the EM algorithm

We consider nonparametric complex spectral estimation of data sequences with missing samples occurring in arbitrary patterns. The existing spectral estimation algorithms designed for uniformly sampled complete-data sequences perform poorly when applied to data sequences with missing samples if the missing samples are simply set to zero. Several nonparametric algorithms have recently been developed to deal with the missing-data problem. They include, for example, GAPES for gapped data and PG-APES, PG-CAPON for periodically gapped data. However, they are not really suitable for the general missing-data problem where the missing data samples occur in arbitrary patterns. In this paper, we deal with a general missing-data spectral estimation problem for which we develop two nonparametric missing-data amplitude and phase estimation (MAPES) algorithms, both of which make use of the expectation maximization (EM) algorithm. Numerical results are provided to demonstrate the effectiveness of the proposed algorithms.

A Consistent Nonparametric Spectral Estimator for Randomly Sampled Signals

In this paper, the nonparametric spectral analysis of a randomly sampled signal is discussed. For this purpose, the general form of Masry's recursive spectral estimators is considered and improved. The corresponding algorithms require the knowledge of the sampling times, the samples, and the sampling law and that the high-frequency decay of the spectrum be at least roughly known. The minimization of the asymptotic equivalent of the mean square estimation error leads to an estimator that is not only consistent but also asymptotically optimal. Theoretical and simulation results regarding this new estimator are given and compared with the standard methods. Besides, the developed theoretical framework strictly includes the case where the sampling time process is Poisson and the signal is Gaussian.

A robust support vector algorithm for nonparametric spectral analysis

We present a new approach to nonparametric spectral estimation on the basis of the support vector method (SVM). A reweighted least squares error formulation avoids the computational limitations of quadratic programming. The application to a synthetic example and to a digital communication problem shows the robustness of the SVM spectral analysis algorithm.

Nonparametric spectral analysis of gapped data via an adaptive filtering approach

We present an algorithm for nonparametric complex spectral analysis of gapped data via an adaptive finite impulse response (FIR) filtering approach, referred to as the gapped-data amplitude and phase estimation (GAPES) algorithm. The incomplete data sequence may contain gaps of various sizes. The GAPES algorithm iterates the following two steps: (1) estimating the adaptive FIR filter and the corresponding complex spectrum via amplitude and phase estimation (APES), a nonparametric adaptive FIR filtering approach, and (2) filling in the gaps via a least-squares APES fitting criterion. The initial condition for the iteration is obtained from the available data segments via APES. Numerical results are presented to demonstrate the effectiveness of the proposed GAPES algorithm.

Estimating Optimal Weights for Instrumental Variable Methods

Stoica, P., and Jansson, M., Estimating Optimal Weights for Instrumental Variable Methods, Digital Signal Processing 11 (2001) 252–268 The accuracy of the instrumental variable approach to parameter estimation (also called correlation analysis) can be significantly improved by optimally weighting the estimating equations. However, the optimal weight in general depends on unknown quantities and hence must be itself estimated before its use becomes possible. The optimal weighting matrix encountered in a typical parameter estimation problem is equal to the DC power of a certain vector sequence and usually it has to be consistently estimated in a nonparametric manner. Consistent nonparametric estimation of power (at any frequency, zero or not) is not an easy task and typically it cannot be achieved by using “natural” estimators (such as the periodogram). Surprisingly, it turns out that in the case considered in this paper there is a natural consistent estimator of the DC power matrix that represents the desired optimal weight. This result will promote the use of optimally weighted parameter estimation methods of instrumental variable or related types; it may also have some interesting consequences for nonparametric spectral analysis which though are not explored herein.

How to improve building thermal simulation programs by use of spectral analysis

The aim of this paper is to demonstrate that non-parametric spectral analysis is a powerful tool for improving simulation models. In the first part of this paper, main theoretical bases are summarised and dedicated tools are defined. The proposed tools are based on the use of ordinary and partial coherence functions and on the identification of frequency responses. A smoothing procedure is used for spectral estimation. In the second part of the paper, the authors use actual data to emphasise the difficulties of spectral analysis, to illustrate the procedure recommended for smoothing spectral estimation and to quantify the variability of the proposed validation tools. The third part of this paper is dedicated to four validation exercises performed on a building thermal simulation program. It is shown how spectral analysis helped in improving the performances of this model by comparing its prediction with actual data issued from three runs involving two buildings.

Advances in processing of surface myoelectric signals: Part 1.

During sustained voluntary or electrically elicited muscle contractions the surface myoelectric signal is nonstationary and it undergoes progressive changes reflecting the modifications of the motor unit action potentials and their propagation velocity. In particular, during sustained electrical stimulation, the evoked signals show progressive amplitude, time scaling and shape modification. The quantitative evaluation of these changes is important for non-invasive muscle characterisation and may be performed in either the time or frequency domain using parametric and nonparametric spectral analysis as well as alternative methodologies. The paper introduces the detection techniques, reviews and compares the methods of spectral estimation based on FFT and autoregressive models, and discusses their applications and limitations in extracting information from the surface myoelectric signal with particular regard to myoelectric manifestations of localised muscle fatigue during sustained contractions.