Showing papers on "Spectral density estimation published in 2019"

A Novel Vital-Sign Sensing Algorithm for Multiple Subjects Based on 24-GHz FMCW Doppler Radar

Abstract: A novel non-contact vital-sign sensing algorithm for use in cases of multiple subjects is proposed. The approach uses a 24 GHz frequency-modulated continuous-wave Doppler radar with the parametric spectral estimation method. Doppler processing and spectral estimation are concurrently implemented to detect vital signs from more than one subject, revealing excellent results. The parametric spectral estimation method is utilized to clearly identify multiple targets, making it possible to distinguish multiple targets located less than 40 cm apart, which is beyond the limit of the theoretical range resolution. Fourier transformation is used to extract phase information, and the result is combined with the spectral estimation result. To eliminate mutual interference, the range integration is performed when combining the range and phase information. By considering breathing and heartbeat periodicity, the proposed algorithm can accurately extract vital signs in real time by applying an auto-regressive algorithm. The capability of a contactless and unobtrusive vital sign measurement with a millimeter wave radar system has innumerable applications, such as remote patient monitoring, emergency surveillance, and personal health care.

Non-Gaussian noise spectroscopy with a superconducting qubit sensor

Abstract: Accurate characterization of the noise influencing a quantum system of interest has far-reaching implications across quantum science, ranging from microscopic modeling of decoherence dynamics to noise-optimized quantum control. While the assumption that noise obeys Gaussian statistics is commonly employed, noise is generically non-Gaussian in nature. In particular, the Gaussian approximation breaks down whenever a qubit is strongly coupled to discrete noise sources or has a non-linear response to the environmental degrees of freedom. Thus, in order to both scrutinize the applicability of the Gaussian assumption and capture distinctive non-Gaussian signatures, a tool for characterizing non-Gaussian noise is essential. Here, we experimentally validate a quantum control protocol which, in addition to the spectrum, reconstructs the leading higher-order spectrum of engineered non-Gaussian dephasing noise using a superconducting qubit as a sensor. This first experimental demonstration of non-Gaussian noise spectroscopy represents a major step toward demonstrating a complete spectral estimation toolbox for quantum devices.

Noise spectral estimation methods and their impact on gravitational wave measurement of compact binary mergers

Abstract: Estimating the parameters of gravitational wave signals detected by ground-based detectors requires an understanding of the properties of the detectors' noise. In particular, the most commonly used likelihood function for gravitational wave data analysis assumes that the noise is Gaussian, stationary, and of known frequency-dependent variance. The variance of the colored Gaussian noise is used as a whitening filter on the data before computation of the likelihood function. In practice the noise variance is not known and it evolves over timescales of dozens of seconds to minutes. We study two methods for estimating this whitening filter for ground-based gravitational wave detectors with the goal of performing parameter estimation studies. The first method uses large amounts of data separated from the specific segment we wish to analyze and computes the power spectral density of the noise through the mean-median Welch method. The second method uses the same data segment as the parameter estimation analysis, which potentially includes a gravitational wave signal, and obtains the whitening filter through a fit of the power spectrum of the data in terms of a sum of splines and Lorentzians. We compare these two methods and conclude that the latter is a more effective spectral estimation method as it is quantitatively consistent with the statistics of the data used for gravitational wave parameter estimation while the former is not. We demonstrate the effect of the two methods by finding quantitative differences in the inferences made about the physical properties of simulated gravitational wave sources added to LIGO-Virgo data.

Ecg classification using higher order spectral estimation and deep learning techniques

Abstract: Electrocardiogram (ECG) is one of the most important and effective tools in clinical routine to assess the cardiac arrhythmias. In this research higherorder spectral estimations, bispectrum and third-order cumulants, are evaluated, saved, and pre-trained using convolutional neural networks (CNN) algorithm. CNN is transferred in this study to carry out automatic ECG arrhythmia diagnostics after employing the higher-order spectral algorithms. Transfer learning strategies are applied on pre-trained convolutional neural network, namely AlexNet and GoogleNet, to carry out the final classification. Five different arrhythmias of ECG waveform are chosen from the MIT-BIH arrhythmia database to evaluate the proposed approach. The main contribution of this study is to utilize the pre-trained convolutional neural networks with a combination of higher-order spectral estimations of arrhythmias ECG signal to implement a reliable and applicable deep learning classification technique. The Highest average accuracy obtained is 97.8 % when using third cumulants and GoogleNet. As is evident from these results, the proposed approach is an efficient automatic cardiac arrhythmia classification method and provides a reliable recognition system based on well-established CNN architectures instead of training a deep CNN from scratch.

Deep Learning Denoising Based Line Spectral Estimation

Abstract: Many well-known line spectral estimators may experience significant performance loss with noisy measurements. To address the problem, we propose a deep learning denoising based approach for line spectral estimation. The proposed approach utilizes a residual learning assisted denoising convolutional neural network (DnCNN) trained to recover the unstructured noise component, which is used to denoise the original measurements. Following the denoising step, we employ a popular model order selection method and a subspace line spectral estimator to the denoised measurements for line spectral estimation. Numerical results show that the proposed approach outperforms a recently introduced atomic norm minimization based denoising method and offers a substantial improvement compared with the line spectral estimation results obtained by directly applying the subspace estimator without denoising.

Spectral density estimation for random fields via periodic embeddings

Abstract: We introduce methods for estimating the spectral density of a random field on a [Formula: see text]-dimensional lattice from incomplete gridded data. Data are iteratively imputed onto an expanded lattice according to a model with a periodic covariance function. The imputations are convenient computationally, in that circulant embedding and preconditioned conjugate gradient methods can produce imputations in [Formula: see text] time and [Formula: see text] memory. However, these so-called periodic imputations are motivated mainly by their ability to produce accurate spectral density estimates. In addition, we introduce a parametric filtering method that is designed to reduce periodogram smoothing bias. The paper contains theoretical results on properties of the imputed-data periodogram and numerical and simulation studies comparing the performance of the proposed methods to existing approaches in a number of scenarios. We present an application to a gridded satellite surface temperature dataset with missing values.

Towards Spectral Estimation from a Single RGB Image in the Wild

Abstract: In contrast to the current literature, we address the problem of estimating the spectrum from a single common trichromatic RGB image obtained under unconstrained settings (e.g. unknown camera parameters, unknown scene radiance, unknown scene contents). For this we use a reference spectrum as provided by a hyperspectral image camera, and propose efficient deep learning solutions for sensitivity function estimation and spectral reconstruction from a single RGB image. We further expand the concept of spectral reconstruction such that to work for RGB images taken in the wild and propose a solution based on a convolutional network conditioned on the estimated sensitivity function. Besides the proposed solutions, we study also generic and sensitivity specialized models and discuss their limitations. We achieve state-of-the-art competitive results on the standard example-based spectral reconstruction benchmarks: ICVL, CAVE and NUS. Moreover, our experiments show that, for the first time, accurate spectral estimation from a single RGB image in the wild is within our reach.

Detection of Periodic Forced Oscillations in Power Systems Using Multitaper Approach

Abstract: An algorithm based on Thomson's multitaper spectral estimation and harmonic analysis techniques is proposed for the detection and frequency estimation of periodic forced oscillations in a power system. Unlike traditional periodogram-based techniques, the method does not rely on true ambient noise spectrum of the system, and can operate continuously in an online environment without requiring any system knowledge except synchrophasor measurements. It compares a test statistic derived from only measurements against a threshold, and the threshold is established from general expressions of the test statistic's distribution and the probability of false alarm. Performance of the detector is explicitly expressed using probability of detection expression, and evaluated using simulation studies. Results upon application of this algorithm to field measured synchrophasor data suggest usability of the technique for forced oscillation detection in practical monitoring of the power system.

Extending comb-based spectral estimation to multiaxis quantum noise

Abstract: We show how to achieve full spectral characterization of general multiaxis additive noise on a single qubit, including arbitrary cross-axis noise correlations. Our pulsed spectral estimation technique is based on sequence repetition and frequency-comb sampling and is applicable in principle even to models where a large qubit energy splitting is present, as long as the noise is stationary and a second-order (Gaussian) approximation to the controlled reduced dynamics is viable. A key innovation in our approach is a spherical representation of the noise in terms of operators that couple directly to raising and lowering qubit operators, which is instrumental to show that only three suitably defined spectra effectively contribute in the large-splitting regime. Our result is crucial to extend the applicability of comb-based spectral estimation, which has been so far employed under the assumption of dephasing-dominated dynamics, to experimental platforms where both ${T}_{1}$ and ${T}_{2}$ processes may occur on comparable timescales or be otherwise significant, such as superconducting qubits.

iMUSIC: A Family of MUSIC-Like Algorithms for Integer Period Estimation

Abstract: The MUSIC algorithm is one of the most popular techniques today for line spectral estimation. If the line spectrum is that of a periodic signal, can we adapt MUSIC to exploit the additional harmonicity in the spectrum? Important prior work in this direction includes the Harmonic MUSIC algorithm and its variations. For applications where the period of the discrete signal is an integer (or can be well approximated by an integer), this paper introduces a new and simpler class of alternatives to MUSIC. This new family, called iMUSIC, also includes techniques where simple integer valued vectors are used in place of complex exponentials for both representing the signal subspace, and for computing the pseudo-spectrum. It will be shown that the proposed methods not only make the computations much simpler than prior periodicity-adaptations of MUSIC, but also offer significantly better estimation accuracies for applications with integer periods. These advantages are demonstrated on examples that include repeats in protein and DNA sequences. The iMUSIC algorithms are based on the recently proposed Ramanujan subspaces and nested periodic subspaces. The resulting signal space bases are non-Vandermonde in structure. Consequently, many aspects of classical MUSIC that were based on the Vandermonde structure of complex-exponentials, such as guarantees for identifiability of the frequencies (periods in our case), are addressed in new ways in this paper.

Fusion of Sensors Data in Automotive Radar Systems: A Spectral Estimation Approach

Abstract: To accurately estimate locations and velocities of surrounding targets (cars) is crucial for advanced driver assistance systems based on radar sensors. In this paper we derive methods for fusing data from multiple radar sensors in order to improve the accuracy and robustness of such estimates. First we pose the target estimation problem as a multivariate multidimensional spectral estimation problem. The problem is multivariate since each radar sensor gives rise to a measurement channel. Then we investigate how the use of the cross-spectra affects target estimates. We see that the use of the magnitude of the cross-spectrum significantly improves the accuracy of the target estimates, whereas an attempt to compensate the phase lag of the cross-spectrum only gives marginal improvement. This paper may be viewed as a first step towards applying high-resolution methods that builds on multidimensional multivariate spectral estimation for sensor fusion.

Bayesian nonparametric spectral density estimation using B-spline priors

Abstract: We present a new Bayesian nonparametric approach to estimating the spectral density of a stationary time series. A nonparametric prior based on a mixture of B-spline distributions is specified and can be regarded as a generalization of the Bernstein polynomial prior of Petrone (Scand J Stat 26:373–393, 1999a; Can J Stat 27:105–126, 1999b) and Choudhuri et al. (J Am Stat Assoc 99(468):1050–1059, 2004). Whittle’s likelihood approximation is used to obtain the pseudo-posterior distribution. This method allows for a data-driven choice of the number of mixture components and the location of knots. Posterior samples are obtained using a Metropolis-within-Gibbs Markov chain Monte Carlo algorithm, and mixing is improved using parallel tempering. We conduct a simulation study to demonstrate that for complicated spectral densities, the B-spline prior provides more accurate Monte Carlo estimates in terms of $$L_1$$ -error and uniform coverage probabilities than the Bernstein polynomial prior. We apply the algorithm to annual mean sunspot data to estimate the solar cycle. Finally, we demonstrate the algorithm’s ability to estimate a spectral density with sharp features, using real gravitational wave detector data from LIGO’s sixth science run, recoloured to match the Advanced LIGO target sensitivity.

Bayesian Spectral Modeling for Multiple Time Series

Abstract: We develop a novel Bayesian modeling approach to spectral density estimation for multiple time series The log-periodogram distribution for each series is modeled as a mixture of Gaussian distribut

Hilbert transform, spectral filters and option pricing

Abstract: We show how spectral filters can improve the convergence of numerical schemes which use discrete Hilbert transforms based on a sinc function expansion, and thus ultimately on the fast Fourier transform. This is relevant, for example, for the computation of fluctuation identities, which give the distribution of the maximum or the minimum of a random path, or the joint distribution at maturity with the extrema staying below or above barriers. We use as examples the methods by Feng and Linetsky (Math Finance 18(3):337–384, 2008) and Fusai et al. (Eur J Oper Res 251(4):124–134, 2016) to price discretely monitored barrier options where the underlying asset price is modelled by an exponential Levy process. Both methods show exponential convergence with respect to the number of grid points in most cases, but are limited to polynomial convergence under certain conditions. We relate these rates of convergence to the Gibbs phenomenon for Fourier transforms and achieve improved results with spectral filtering.

RF-Based Noncontact Respiratory Rate Monitoring With Parametric Spectral Estimation

Abstract: Respiratory rate (RR) monitoring of an adult or an infant during sleep or in steady position can be lifesaving, especially in home care systems. In this paper, we examine the potentials of wireless radio frequency (RF) signals to monitor the RR. A new noncontact RR monitoring system is proposed. The system includes a simple motion detection algorithm based on adaptive thresholding to eliminate the effects of the large-scale body movements on the RR estimation. In the proposed system, the high resolution subspace-based parametric spectral estimation approaches, estimation of signal parameters by rotational invariance technique (ESPRIT) and multiple signal classification (MUSIC), are presented as the RR estimation algorithms. According to our knowledge, the ESPRIT algorithm, which estimates the spectrum without searching, is used for the first time in this paper for RR estimation. It is shown that ESPRIT is computationally efficient and works approximately 49 times faster than the MUSIC algorithm. It is also shown with various experiments conducted with ten volunteers that the proposed noncontact RR monitoring system attains 0.13 breath per minute (bpm) error rate with the limited number of data and outperforms the periodogram method commonly used as the benchmark.

A New Approach to ARMAX Signals Smoothing: Application to Variable-Q ARMA Filter Design

Abstract: In this paper, we propose a new approach to signal smoothing when the data are generated (or represented) by an autoregressive moving average with exogenous inputs (ARMAX) model. In this approach, the original ARMAX recurrence relation is directly employed and combined with a constrained least squares optimization framework to filter out both system and measurement noise components and estimate the desired signal in form of block-wise matrix formulation. The approach is also driven from a forward backward filtering, which is accomplished through linear time invariant system. While the impulse response of the proposed filter can be found using deconvolution operator, a closed-form expression is presented for its impulse response without resorting to any transform methods. Two examples of its applications for variable-Q filter design and spectral density estimation are given, which demonstrate the present approach is more effective and robust than the existing variable-Q filter designs in the literature and it can be used to improve the spectral density estimation.

Low Complexity and High-Resolution Line Spectral Estimation Using Cyclic Minimization

Abstract: The line spectral estimation problem has applications in radar, wireless communications, spectroscopy, and power electronics, among others. The signal is modeled as a sparse linear combination of complex sinusoids and the problem target is to estimate the number of sinusoids in the mixture, and respective parameters of each individual sinusoid, such as magnitude, phase, and frequency. In this work, we first introduce a novel formulation of the rank function, which involves the solution of a multi-convex optimization problem. Using the multi-convex reformulation of the rank function an over-parameterization of the line estimation problem is proposed together with a cyclic minimization procedure to obtain a solution. The cyclic method iterates between the optimization of the signal subspace and null-space and stops when the two are orthogonal. Every limit point of the sequence of iterates is shown to be a stationary point of the original problem. Numerical experiments show that only a small number of iterations is required for convergence. The signal subspace optimization is a semidefinite program (SDP) and the null-space optimization has a closed-form solution. The cost per iteration of a general-purpose interior point method (IPM) to solve the SDP is a quartic function of the problem dimension. It is shown that by exploiting the problem structure the cost per iteration of the IPM may be reduced to a cubic function of the problem dimension, comparable to the cost of the alternating direction method of multipliers (ADMM). However, contrarily to the latter, the former achieves the precision necessary for fine frequency localization. A large set of numerical experiments show the effectiveness of the proposed approach.

Generalized Time-Updating Sparse Covariance-Based Spectral Estimation

Abstract: Recently, the time-updating q -norm sparse covariance-based estimator (q -SPICE) was developed for online spectral estimation of stationary signals. In this work, this development is furthered to deal with non-stationary signals. By introducing a weighting matrix defined by a forgetting factor, the generalized least absolute shrinkage and selection operator (LASSO) is generalized, in order to allow for changes in the spectral content. As shown here, the resulting LASSO formulation can be solved in a simple manner using cyclic minimization, enabling recursive estimation for non-stationary signals. The proposed generalized time-updating q -SPICE offers the same benefits as the original estimator, including being computationally efficient at constant computational and storage cost, but also allows for substantial improvements when dealing with non-stationary signals. The performance of the method is evaluated using both stationary and non-stationary signals, indicating the preferable performance of the generalized formulation as compared to the original time-updating SPICE algorithm.

Criterion of Significance Level for Selection of Order of Spectral Estimation of Entropy Maximum

Abstract: It is researched a wide class of parametric estimations of power spectral density based on principle of entropy maximum and autoregression observation model. At that there is distinguished the key parameter which is used model order. It is considered a problem of a priori uncertainty when true value of order is a priori unknown. It is proposed a new criterion for definition of order using finite sampling volume with purpose of overcome of the drawbacks of existing algorithms in conditions of small sampling. The principle of guaranteed significance level in a problem of complex statistic hypothesis verification is a basic principle of this criterion. In contrast to criteria of AIC, BIC, etc. this criterion is not related to determination of measurements inaccuracy, since it uses a conception of “significance level” of formed solution only. The efficiency of proposed criterion is researched theoretically and experimentally. An example of its application in a problem of spectral analysis of voice signals is considered. Recommendations about its practical application in the systems of digital signal processing are given.

Improved Blind Timing Skew Estimation Based on Spectrum Sparsity and ApFFT in Time-Interleaved ADCs

Abstract: Timing skews among channels degrade seriously the time-interleaved analog-to-digital converter (TIADC) performance, which can be improved by the blind timing skew estimation (TSE) technique. In this paper, we proposed the all-phase fast Fourier transform (ApFFT) based on spectrum sparsity signal phase relationship blind TSE (ApFFT-SSPR-BLTSE) algorithm. The ApFFT-SSPR-BLTSE algorithm reduces computational complexity based on the phase relationship of the total output from TIADC and the corresponding reference channel output compared with the existing spectrum sparsity blind TSE (SS-BLTSE) algorithm. We also utilized the ApFFT technique to increase the accuracy of phase spectral estimation. Simulation results show that the proposed ApFFT-SSPR-BLTSE algorithm, which as a reduced number of fast Fourier transforms (FFTs) and low hardware complexity, has higher accuracy for blind TSE compared to the existing SS-BLTSE algorithm. In addition, this paper presents an efficient hardware architecture of the ApFFT-SSPR-BLTSE algorithm on the Xilinx Virtex-6 vlx550tff1759 field-programmable gate array (FPGA) chip for the blind TSE of the four-channel 400-MHz 14-bit TIADC real system. The validation results show that the proposed algorithm uses only a few percent of the hardware resources of the FPGA chip, and the mismatch spurs were suppressed to better than −81.54 dB.

Spectral and Time-Frequency Analysis

Abstract: EEG signals are typically characterized by oscillatory patterns at certain frequency bands. Normally, the EEG data, especially spontaneous EEG data, are analyzed in the frequency domain. The spectral analysis can transform EEG signals from time domain to the frequency domain, which can reveal how the power of EEG signals is distributed along frequencies. Furthermore, as EEG spectrum could substantially vary over time, joint time-frequency analysis is often used to reveal time-varying spectral activities of EEG. Particularly, time-frequency analysis is a powerful method to estimate the event-related EEG spectral patterns, i.e., event-related synchronization/desynchronization (ERS/ERD). In this chapter, I introduce some commonly used spectral estimation methods (e.g., the periodogram, the Welch’s method, and the multitaper method) and time-frequency analysis methods (e.g., short-time Fourier transform and continuous wavelet transform). We also raise some practical issues and cautionary notes when using these methods on EEG data analysis, such as parameter tuning, visualization, and results reporting.

QLSA: A Software Library for Spectral Estimation in Low-Frequency Noise Measurement Applications

Abstract: A public domain software library is introduced and discussed that aims at enabling the development of customized real-time spectral analysis applications in the field of Low-Frequency Noise Measure...

M$^2$-Spectral Estimation: A Relative Entropy Approach

Abstract: This paper deals with M$^2$-signals, namely multivariate (or vector-valued) signals defined over a multidimensional domain. In particular, we propose an optimization technique to solve the covariance extension problem for stationary random vector fields. The multidimensional Itakura-Saito distance is employed as an optimization criterion to select the solution among the spectra satisfying a finite number of moment constraints. In order to avoid technicalities that may happen on the boundary of the feasible set, we deal with the discrete version of the problem where the multidimensional integrals are approximated by Riemann sums. The spectrum solution is also discrete, which occurs naturally when the underlying random field is periodic. We show that a solution to the discrete problem exists, is unique and depends smoothly on the problem data. Therefore, we have a well-posed problem whose solution can be tuned in a smooth manner. Finally, we have applied our theory to the target parameter estimation problem in an integrated system of automotive modules. Simulation results show that our spectral estimator has promising performance.

Audio-Noise Power Spectral Density Estimation Using Long Short-Term Memory

Abstract: We propose a method using a long short-term memory (LSTM) network to estimate the noise power spectral density (PSD) of single-channel audio signals represented in the short-time Fourier transform (STFT) domain. An LSTM network common to all frequency bands is trained, which processes each frequency band individually by mapping the noisy STFT magnitude sequence to its corresponding noise PSD sequence. Unlike deep-learning-based speech-enhancement methods, which learn the full-band spectral structure of speech segments, the proposed method exploits the sub-band STFT magnitude evolution of noise with long time dependence, in the spirit of the unsupervised noise estimators described in the literature. Speaker- and speech-independent experiments with different types of noise show that the proposed method outperforms the unsupervised estimators, and it generalizes well to noise types that are not present in the training set.

Fast Multitaper Spectral Estimation

Abstract: Thomson’s multitaper method using discrete prolate spheroidal sequences (DPSSs) is a widely used technique for spectral estimation. For a signal of length N, Thomson’s method requires selecting a bandwidth parameter W, and then uses K ≈ 2NW tapers. The computational cost of evaluating the multitaper estimate at N grid frequencies is O(KN log N). It has been shown that the choice of W and K which minimizes the MSE of the multitaper estimate is W = O(N−1/5) and K = O(N4/5). This choice would require a computational cost of O(N9/5 log N). We demonstrate an ϵ-approximation to the multitaper estimate which can be evaluated at N grid frequencies using $O\left( {N{{\log }^2}N\log \frac{1}{\varepsilon }} \right)$ operations.

Research on Rough and Detailed Combination Spectrum Analysis of Electromagnetic Signals Based on Complex Modulation ZoomFFT

Abstract: Electromagnetic spectrum sensing requires spectral estimation of electromagnetic signals in the environment. In traditional FFT methods, frequency spectral resolution and computational quantities are mutually constrained. In this paper, a method of combining the roughly and the finicky analysis is proposed. After the rough panoramic spectrum analysis is performed by FFT, the fine spectrum analysis of the selected frequency band is performed. The combination of the two methods can obtain a large-scale spectrum distribution and a local detailed spectrum distribution. In this paper, the spectrum analysis of the rough and detailed combination analysis of the electromagnetic signals obtained by the actual acquisition is simulated.