Showing papers on "Spectral density estimation published in 2015"
TL;DR: This paper presents a gridless version of SPICE (gridless SPICE, or GLS), which is applicable to both complete and incomplete data without the knowledge of noise level, and proves the equivalence between GLS and atomic norm-based techniques under different assumptions of noise.
Abstract: This paper is concerned about sparse, continuous frequency estimation in line spectral estimation, and focused on developing gridless sparse methods which overcome grid mismatches and correspond to limiting scenarios of existing grid-based approaches, e.g., $\ell_{1}$ optimization and SPICE, with an infinitely dense grid. We generalize AST (atomic-norm soft thresholding) to the case of nonconsecutively sampled data (incomplete data) inspired by recent atomic norm based techniques. We present a gridless version of SPICE (gridless SPICE, or GLS), which is applicable to both complete and incomplete data without the knowledge of noise level. We further prove the equivalence between GLS and atomic norm-based techniques under different assumptions of noise. Moreover, we extend GLS to a systematic framework consisting of model order selection and robust frequency estimation, and present feasible algorithms for AST and GLS. Numerical simulations are provided to validate our theoretical analysis and demonstrate performance of our methods compared to existing ones.
235 citations
TL;DR: In this paper, a multicomponent, variable dimension, parametrized model is proposed to describe the Gaussian-noise power spectrum for data from ground-based gravitational wave interferometers.
Abstract: Gravitational wave data from ground-based detectors is dominated by instrument noise. Signals will be comparatively weak, and our understanding of the noise will influence detection confidence and signal characterization. Mismodeled noise can produce large systematic biases in both model selection and parameter estimation. Here we introduce a multicomponent, variable dimension, parametrized model to describe the Gaussian-noise power spectrum for data from ground-based gravitational wave interferometers. Called BayesLine, the algorithm models the noise power spectral density using cubic splines for smoothly varying broadband noise and Lorentzians for narrow-band line features in the spectrum. We describe the algorithm and demonstrate its performance on data from the fifth and sixth LIGO science runs. Once fully integrated into LIGO/Virgo data analysis software, BayesLine will produce accurate spectral estimation and provide a means for marginalizing inferences drawn from the data over all plausible noise spectra.
212 citations
TL;DR: In this article, a nearly optimal algorithm for denoising a mixture of sinusoids from noisy equispaced samples was derived by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary.
Abstract: This paper establishes a nearly optimal algorithm for denoising a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary. We show how to compute the estimator via semidefinite programming and provide guarantees on its mean-squared error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semidefinite programming approach outperforms three classical spectral estimation techniques.
159 citations
TL;DR: The results demonstrate clearly that the proposed methodology is immune to noise and capable of estimating the optimal boundaries to isolate the frequencies from noise and estimate the main frequencies with high accuracy, especially the closely-spaced frequencies.
141 citations
TL;DR: In this article, a parametric spectral estimator based on the maximum likelihood estimator (MLE) was proposed for fault detection in electrical machines, which is evaluated using simulation signals, issued from a coupled electromagnetic circuits approach-based simulation tool.
97 citations
TL;DR: In this paper, a novel direction-finding method by the time-modulated array (TMA) is proposed through analyzing the harmonic characteristic of received signal, which requires only two antenna elements and a single RF channel.
Abstract: A novel direction-finding method by the time-modulated array (TMA) is proposed through analyzing the harmonic characteristic of received signal, which requires only two antenna elements and a single RF channel. The signal processing of the proposed method is concise, and its calculation amount concentrates on a two-point discrete Fourier transform (DFT). Numeric simulations are provided to examine the performance of the proposed method, and a simple S band two-element TMA is constructed and tested to verify its effectiveness.
84 citations
TL;DR: A new divergence family is derived between multivariate spectral densities which takes root in the prediction theory and under mild assumptions on the a priori spectral density, the approximation problem admits a family of solutions.
Abstract: In this technical note, we deal with a spectrum approximation problem arising in THREE-like multivariate spectral estimation approaches. The solution to the problem minimizes a suitable divergence index with respect to an a priori spectral density. We derive a new divergence family between multivariate spectral densities which takes root in the prediction theory. Under mild assumptions on the a priori spectral density, the approximation problem, based on this new divergence family, admits a family of solutions. Moreover, an upper bound on the complexity degree of these solutions is provided.
76 citations
TL;DR: In this article, the Ablowitz-Ladik decision was applied to coherently detected short 16GBd BPSK sequences after transmission over a few spans of standard SMF fiber in lab.
Abstract: The Ablowitz–Ladik—a mathematical tool for calculating the nonlinear Fourier transform (NFT) of a time-domain signal—is applied to coherently detected short 16-GBd BPSK sequences after transmission over a few spans of standard SMF fiber in lab. Decision schemes are investigated, which compare the nonlinear spectrum of received signal blocks consisting of a sequence of four BPSK symbols with a set of calculated reference spectra. Decision on the continuous part of the NFT spectrum was successfully demonstrated. At higher signal power performance, degradation was linked to peaks in the continuous amplitude spectrum. They are emerging at large signal noise and change depending on the noise seed and lead to an increased variance of the minimum distance criterion which was applied for decision. Decision based on the discrete part of the nonlinear spectrum worked successfully at high signal power. In particular, the position of one or more eigenvalues in the complex plane, referred to as eigenvalue pattern, exhibited a low variance for signal with noise and enable low error rate. However, the measurements also show that with increasing signal power, link length, and noise, the reliability of the proposed detection is limited, and further refinement of decision criteria seems necessary.
72 citations
TL;DR: A synchronized phase and frequency estimation algorithm suitable for measurement at the distribution level is proposed and tested under noise and harmonic conditions, as well as various conditions in the phasor measurement unit Standard, to verify its measurement accuracy at the Distribution level.
Abstract: This paper proposes a method for estimating synchronized phase and frequency at the distribution level under both steady-state and dynamic conditions. The discrete Fourier transform-based method is widely used for phasor and frequency estimation, thanks to its low computational burden. However, errors arise when the power system is operating at off-nominal frequency, especially under dynamic conditions such as phase modulation. Additionally, the power grid signal at the distribution level contains more noise and harmonics, which cause phase and frequency estimation errors. In this paper, a synchronized phase and frequency estimation algorithm suitable for measurement at the distribution level is proposed and tested under noise and harmonic conditions, as well as various conditions in the phasor measurement unit Standard (C37.118.1-2011 and C37.118.1a-2014), to verify its measurement accuracy at the distribution level.
71 citations
TL;DR: Theoretical analysis shows that the NSTFT method is independent of the signal amplitude and is only relevant to the signal phase, thus it can be used for weak signal detection.
67 citations
TL;DR: A D-fold Hankel matrix is constructed from the measurements and exploited to exploit its Vandermonde decomposition in the noiseless case, and numerical experiments show that the noise tolerance of MUSIC obeys a power law with the minimum separation of frequencies.
Abstract: This paper presents a performance analysis of the MUltiple SIgnal Classification (MUSIC) algorithm applied on $D$ dimensional single-snapshot spectral estimation while $s$ true frequencies are located on the continuum of a bounded domain. Inspired by the matrix pencil form, we construct a D-fold Hankel matrix from the measurements and exploit its Vandermonde decomposition in the noiseless case. MUSIC amounts to identifying a noise subspace, evaluating a noise-space correlation function, and localizing frequencies by searching the $s$ smallest local minima of the noise-space correlation function. In the noiseless case, $(2s)^{D}$ measurements guarantee an exact reconstruction by MUSIC as the noise-space correlation function vanishes exactly at true frequencies. When noise exists, we provide an explicit estimate on the perturbation of the noise-space correlation function in terms of noise level, dimension $D$ , the minimum separation among frequencies, the maximum and minimum amplitudes while frequencies are separated by 2 Rayleigh Length (RL) at each direction. As a by-product the maximum and minimum non-zero singular values of the multidimensional Vandermonde matrix whose nodes are on the unit sphere are estimated under a gap condition of the nodes. Under the 2-RL separation condition, if noise is i.i.d. Gaussian, we show that perturbation of the noise-space correlation function decays like $\sqrt{\log(\#({\bf N}))/\#({\bf N})}$ as the sample size $\#({\bf N})$ increases. When the separation among frequencies drops below 2 RL, our numerical experiments show that the noise tolerance of MUSIC obeys a power law with the minimum separation of frequencies.
TL;DR: In this paper, a rate-optimal estimator of the entire quadratic covariation of an Ito-semimartingale is constructed by a locally adaptive spectral approach.
TL;DR: A method for accurate and efficient parameter estimation and decomposition of sinusoidally frequency modulated signals is presented and theory is illustrated on signals with one and more components, including noise and disturbances, as well as time-frequency patterns that deviate from sinusoidal form.
Abstract: A method for accurate and efficient parameter estimation and decomposition of sinusoidally frequency modulated signals is presented. These kinds of signals are of special interest in radars and communications. The proposed method is based on the inverse Radon transform property to transform a two-dimensional sinusoidal pattern into a single point in a two-dimensional plane. Since the signal is well concentrated (sparse) in the inverse Radon transform domain, its reconstruction can be performed from a reduced set of observations (back-projections). Theory is illustrated on signals with one and more components, including noise and disturbances, as well as time-frequency patterns that deviate from sinusoidal form.
TL;DR: In this paper, a positive-sequence phase-angle estimation method based on discrete Fourier transform for the synchronization of three-phase power-electronic converters under distorted and variable-frequency conditions is proposed.
Abstract: This paper proposes a positive-sequence phase-angle estimation method based on discrete Fourier transform for the synchronization of three-phase power-electronic converters under distorted and variable-frequency conditions. The proposed method is designed based on a fixed sampling rate and, thus, it can simply be employed for control applications. First, analytical analysis is presented to determine the errors associated with the phasor estimation using standard discrete Fourier transform in a variable-frequency environment. Then, a robust phase-angle estimation technique is proposed, which is based on a combination of estimated positive and negative sequences, tracked frequency, and two proposed compensation coefficients. The proposed method has one cycle transient response and is immune to harmonics, noises, voltage imbalances, and grid frequency variations. An effective approximation technique is proposed to simplify the computation of the compensation coefficients. The effectiveness of the proposed method is verified through a comprehensive set of simulations in Matlab software. Simulation results show the robust and accurate performance of the proposed method in various abnormal operating conditions.
TL;DR: It is concluded that the estimation techniques tested are not sufficiently accurate when compared with the measured ground truth data and that there remains significant scope to improve estimation algorithms for spectral estimation.
Abstract: In this article, we describe a spectral sensitivity measurement procedure at the National Physical Laboratory, London, with the aim of obtaining ground truth spectral sensitivity functions for Nikon D5100 and Sigma SD1 Merill cameras. The novelty of our data is that the potential measurement errors are estimated at each wavelength. We determine how well the measured spectral sensitivity functions represent the actual camera sensitivity functions (as a function of wavelength). The second contribution of this paper is to test the performance of various leading sensor estimation techniques implemented from the literature using measured and synthetic data and also evaluate them based on ground truth data for the two cameras. We conclude that the estimation techniques tested are not sufficiently accurate when compared with our measured ground truth data and that there remains significant scope to improve estimation algorithms for spectral estimation. To help in this endeavor, we will make all our data available online for the community.
TL;DR: It is shown that an OFDM signal after passing through the MSML channel exhibits a low rank representation, and two strategies using convex and no-convex regularizers to remove noise from the corrupted signal are proposed.
Abstract: This paper considers the estimation of multi-scale multi-lag (MSML) channels. The MSML channel model is a good representation for wideband communication channels, such as underwater acoustic communication and radar. This model is characterized by a limited number of paths, each parameterized by a delay, Doppler scale, and attenuation factor. Herein, it is shown that an OFDM signal after passing through the MSML channel exhibits a low rank representation. This feature can be exploited to improve the channel estimation. By characterizing the received signal, it is shown that the MSML channel estimation problem can be adapted to a structured spectral estimation problem. The challenge is that the unknown frequencies are very close to each other due to the small values of Doppler scales. This feature can be employed to show that the data matrix is approximately low-rank. By exploiting structural features of the received signal, the Prony algorithm is modified to estimate the Doppler scales (close frequencies), delays and channel gains. Two strategies using convex and no-convex regularizers to remove noise from the corrupted signal are proposed. These algorithms are iterative based on the alternating direction method of multipliers. A bound on the reconstruction of the noiseless received signal provides guidance on the selection of the relaxation parameter in the optimizations. The performance of the proposed estimation strategies are investigated via numerical simulations, and it is shown that the proposed non-convex method offers up to 7 dB improvement in low SNR and the convex method offers up to 5 dB improvement in high SNR over prior methods for the MSML channel estimation.
TL;DR: In this paper, a modified Prony method was proposed for the estimation of the frequencies and amplitudes of broken rotor bar faults using a linear time-frequency/amplitude representation with high frequency resolution and adjustable time resolution.
Abstract: The knowledge of the broken rotor bar characteristic frequencies and amplitudes has a great importance for all related diagnostic methods. The monitoring of motor faults requires a high resolution spectrum to separate different frequency components. The discrete Fourier transform (DFT) has been widely used to achieve these requirements. However, DFT can give meaningful information only for stationary harmonics which cannot be guaranteed in real cases. In addition, a long data sequence is necessary for DFT to get high frequency resolution. Nevertheless, the signals are time varying, and the steady-state conditions can be lost for a long time acquisition. As a solution for these problems, this paper proposes an efficient time-domain technique based on a modified Prony method for the estimation of the frequencies/amplitudes of broken rotor bar faults. Using this technique, the stator current is divided into short overlapped time windows, and each one is analyzed by the least squares Prony method. The proposed technique provides a linear time–frequency/amplitude representation with high frequency resolution and adjustable time resolution. It is shown that this technique allows tracking the frequencies and amplitudes of the sidebands around the fundamental frequency component with a very high accuracy. The efficiency of the proposed method is verified by simulation and experimental tests.
TL;DR: In this paper, the authors show that the dual problem can be seen as a new parametric spectral estimation problem, which is optimal in terms of closeness to the correlogram over a certain parametric class of spectral densities describing ARMA models, enriching in this way its meaningfulness.
17 Oct 2015
TL;DR: In this paper, the authors presented an algorithm for robustly computing sparse Fourier transforms in the continuous setting, with sample complexity linear in k and logarithmic in the signal-to-noise ratio and the frequency resolution.
Abstract: In recent years, a number of works have studied methods for computing the Fourier transform in sub linear time if the output is sparse. Most of these have focused on the discrete setting, even though in many applications the input signal is continuous and naive discretization significantly worsens the sparsity level. We present an algorithm for robustly computing sparse Fourier transforms in the continuous setting. Let x(t) = x*(t) + g(t), where x* has a k-sparse Fourier transform and g is an arbitrary noise term. Given sample access to x(t) for some duration T, we show how to find a k-Fourier-sparse reconstruction x'(t) with [frac{1}{T}int0T abs{x(t) - x(t)}2 mathrm{d} t lesssim frac{1}{T}int0T abs{g(t)}2 mathrm{d}t. The sample complexity is linear in k and logarithmic in the signal-to-noise ratio and the frequency resolution. Previous results with similar sample complexities could not tolerate an infinitesimal amount of i.i.d. Gaussian noise, and even algorithms with higher sample complexities increased the noise by a polynomial factor. We also give new results for how precisely the individual frequencies of x* can be recovered.
TL;DR: A high-resolution time-frequency transform is used to achieve separation and identification of Pand S-waves with subtly different frequency contents that would not be recoverable using short-term Fourier transforms due to its smearing in the frequency domain.
Abstract: Separation of a seismogram into its individual constitutive phases (Pand S-wave arrivals, surface waves, etc.) is a long-standing problem. In this letter, we use a high-resolution time-frequency transform to achieve this and reconstruct their individual waveforms in the time domain. The procedure is illustrated using microseismic events recorded during a hydraulic fracturing treatment. The synchrosqueezing transform is an extension of the continuous wavelet transform combined with frequency reassignment. Its high-resolution time-frequency decompositions allow for separation and identification of Pand S-waves with subtly different frequency contents that would not be recoverable using short-term Fourier transforms due to its smearing in the frequency domain. It is an invertible transform, thus allowing for signal reconstruction in the time domain after signal separation. The same approach is applicable to other seismic signals such as resonance frequencies and long-period events and offers promising new possibilities for enhanced signal interpretation in terms of underlying physical processes.
TL;DR: A frequency-adaptive robust technique for the accurate estimation of the single-phase grid voltage fundamental and harmonic parameters, based on the discrete Fourier transform and a cascaded delayed signal cancellation strategy is reported.
Abstract: This paper reports a frequency-adaptive robust technique for the accurate estimation of the single-phase grid voltage fundamental and harmonic parameters. The technique is based on the discrete Fourier transform and a cascaded delayed signal cancellation strategy. There is no stability issue in the technique, since it does not contain any type of feedback loop. It can also be flexibly configured to estimate the parameters of the fundamental and/or one/multiple harmonic(s) from the grid voltage waveform distorted by various harmonics. Moreover, it does not require evaluation of trigonometric and inverse trigonometric functions for implementing on real-time digital signal processor. However, it needs computationally demanding high-order finite-impulse-response filters. The simulation and real-time experimental results are provided to verify the performance of the proposed technique.
TL;DR: SE-O CT breaks the coherence length limitation and improves the axial resolution by a factor of up to 4.7 compared with FD-OCT, and provides complete sidelobe suppression in the depth point-spread function, further improving the image quality.
Abstract: The depth reflectivity profile of Fourier domain optical coherence tomography (FD-OCT) is estimated from the inverse Fourier transform of the spectral interference signals (interferograms). As a result, the axial resolution is fundamentally limited by the coherence length of the light source. We demonstrate that using the autoregressive spectral estimation technique instead of the inverse Fourier transform, to analyze the spectral interferograms can improve the axial resolution. We name this method spectral estimation OCT (SE-OCT). SE-OCT breaks the coherence length limitation and improves the axial resolution by a factor of up to 4.7 compared with FD-OCT. Furthermore, SE-OCT provides complete sidelobe suppression in the depth point-spread function, further improving the image quality. We demonstrate that these technical advances enables clear identification of corneal endothelium anatomical details ex vivo that cannot be identified using the corresponding FD-OCT. Given that SE-OCT can be implemented in the FD-OCT devices without any hardware changes, the new capabilities provided by SE-OCT are likely to offer immediate improvements to the diagnosis and management of diseases based on OCT imaging.
TL;DR: For the first time, it is shown how to design the kernel of the transform and specifically, the nonlinear group delay profile dictated by the signal sparsity, leading to smart stretching with nonuniform spectral resolution, having direct utility in improvement of data acquisition rate, real-time data compression, and enhancement of ultrafast data capture accuracy.
Abstract: Time stretch dispersive Fourier transform enables real-time spectroscopy at the repetition rate of million scans per second. High-speed real-time instruments ranging from analog-to-digital converters to cameras and single-shot rare-phenomena capture equipment with record performance have been empowered by it. Its warped stretch variant, realized with nonlinear group delay dispersion, offers variable-rate spectral domain sampling, as well as the ability to engineer the time-bandwidth product of the signal’s envelope to match that of the data acquisition systems. To be able to reconstruct the signal with low loss, the spectrotemporal distribution of the signal spectrum needs to be sparse. Here, for the first time, we show how to design the kernel of the transform and specifically, the nonlinear group delay profile dictated by the signal sparsity. Such a kernel leads to smart stretching with nonuniform spectral resolution, having direct utility in improvement of data acquisition rate, real-time data compression, and enhancement of ultrafast data capture accuracy. We also discuss the application of warped stretch transform in spectrotemporal analysis of continuous-time signals.
TL;DR: In this paper, the authors considered noisy non-synchronous discrete observations of a continuous semimartingale with random volatility and established functional stable central limit theorems under high-frequency asymptotics in three setups: one dimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous observations for a bivariate spectral covolatility estimator and multivariate for a local method of moments.
10 May 2015
TL;DR: A novel algorithm that combines segmented discrete polynomial-phase transform and sparse discrete fractional Fourier transform is proposed to yield a significant reduction of the computational load with a satisfactory estimation performance.
Abstract: This paper addresses the problem of estimating the chirp rates of multi-component linear frequency modulated signals, which is important in radar, sonar and navigation signal processing The main difficulties in the estimation procedure lie in the cross-terms between multi-components and the high computation burden To solve these problems, a novel algorithm that combines segmented discrete polynomial-phase transform and sparse discrete fractional Fourier transform is proposed to yield a significant reduction of the computational load with a satisfactory estimation performance Simulation results are provided to demonstrate the effectiveness of the proposed approach
TL;DR: In this article, the fractal properties of the power spectrum of sea clutter were analyzed using autoregressive (AR) spectrum estimation and a novel weak target detection method based on AR Hurst exponent was proposed.
Abstract: This study concerns the fractal properties of sea clutter in the power spectrum domain. To overcome the deficiencies of Fourier transform analysis, the power spectrum of the sea clutter is obtained by autoregressive (AR) spectrum estimation. The AR model is a linear predictive model, which estimates the power spectrum of sea clutter form its autocorrelation matrix and has a higher frequency resolution than Fourier analysis. This study concentrates on analysing the fractal property of the power spectrum based on AR spectral estimation and its application on weak target detection. First, fractional Brownian motion is taken as an example to prove the fractal property of the power spectrum. Then, real measured X-band data is used to verify the fractal property of the power spectrum of sea clutter. Finally, a novel detection method based on AR Hurst exponent is proposed and the factors influencing the fractal properties of power spectrum are analysed. The results show that the Hurst exponent of AR spectrum is effective for weak target detection in sea clutter background. Compared with the existing fractal method and the traditional constant false alarm rate (CFAR) method, the proposed method has a better detection performance.
Patent•
30 Jun 2015TL;DR: In this paper, a spectral estimation method using multiple, poly-energetic x-ray sources to generate x-rays and to direct the xrays towards a target object is disclosed. And the method also includes estimating cross-sectional images of the target object based on the polyenergetic measurements.
Abstract: Spectral estimation and poly-energetic reconstructions methods and x-ray systems are disclosed. According to an aspect, a spectral estimation method includes using multiple, poly-energetic x-ray sources to generate x-rays and to direct the x-rays towards a target object. The method also includes acquiring a series of poly-energetic measurements of x-rays from the target object. Further, the method includes estimating cross-sectional images of the target object based on the poly-energetic measurements. The method also includes determining path lengths through the cross-sectional images. Further, the method includes determining de-noised poly-energetic measurements and de-noised path lengths based on the acquired poly-energetic measurements and the determined path lengths. The method also includes estimating spectra for angular trajectories of a field of view based on the de-noised poly-energetic measurements and the path lengths.
TL;DR: The preliminary results of this study indicate that applying the first and second derivatives to PPG waveforms is useful for determining heat stress level using 20-s recordings and Welch's and Yule-Walker's methods in agreement that the second derivative is an improved detector for heat stress are in agreement.
TL;DR: The proposed IpDFT algorithm has better antinoise capability and computational efficiency than the optimization-based algorithm by Radil, and it is illustrated that the simulation results agree well with upper and lower bounds of the theoretical variance.
Abstract: In this paper, a scale factor-based interpolated discrete Fourier transform (IpDFT) algorithm is proposed to estimate the dominant chatter frequency. In practical measurement systems of machining processes, the number of acquired sine-wave cycles (NASCs) is small. Therefore, the significant spectral interference from the negative frequency leads to the degradation of conventional IpDFTs that neglect such interference. The proposed IpDFT algorithm overcomes this problem by completely removing the long-range leakage of the negative frequency of the investigated component. We establish statistical properties of the approach contaminated with white noise, including upper and lower bounds of the theoretical variance. The simulation results demonstrate that our IpDFT algorithm outperforms existing IpDFT algorithms, especially when the NASC approaches zero. The proposed IpDFT algorithm has better antinoise capability and computational efficiency than the optimization-based algorithm by Radil. Furthermore, it is illustrated that the simulation results agree well with upper and lower bounds of the theoretical variance. Cutting force signals are collected to evaluate the algorithm experimentally.
TL;DR: This paper proposes an iterative frequency estimation algorithm based on the interpolation of Fourier coefficients of weighted samples that is compatible with all conventional window functions and demonstrates that errors caused by a mistaken location of the spectral line can be significantly reduced.