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We consider the estimation of the covariance of a stationary Gaussian process on a multi-dimensional grid from observations taken on a general acquisition domain. We derive spectral-norm risk rates for multi-taper estimators. When applied to one dimensional acquisition intervals, these show that Thomson's classical multi-taper has optimal risk rates, as they match known benchmarks. We also extend existing lower risk bounds to multi-dimensional grids and conclude that multi-taper estimators associated with certain two-dimensional acquisition domains also have almost optimal risk rates.

Hidden Markov Models (HMM) are widely used to represent time series with regime switching phenomenon. The most popular inference method of HMM is the Baum-Welch (B-W) algorithm, which is a special case of the E-M algorithm. However, it can be too slow for many real-time applications and is prone to being trapped into local optima. Spectral learning of HMM (SHMM), which is based on the method of moments estimation, has been proposed in the literature to overcome these obstacles. Despite its promises, asymptotic theory for SHMM has been elusive, and the long-run performance of SHMM can degrade due to unchecked propagation of error. In this thesis, for spectral estimation, we studied the theoretical property of the approximation error, improved the spectral learning by adding a 'project-onto-simplex' regularization, and provided the online learning of SHMM. We compare the performance of the proposed method with the state-of-the-art methods on both simulated data and real world applications, and find that the new method not only retains the computational advantages of SHMM, but also provides more robust estimation and forecasting. SHMM is dedicated to the endogenous evolution of HMM. Some HMM's evolution is impacted by cross predictors. We propose a variant of HMM called latent control HMM, which provides a binary latent variable controlling whether each cross predictor has impact on the transition or not. This model is inferred by standard Markov Chain Monte Carlo (MCMC) sampling, which provides the predictability and interpretability. We show the latent control HMM's performance on both simulated and real-world data sets.

The Unlimited Sensing Framework (USF) is a digital acquisition protocol that allows for sampling and reconstruction of high dynamic range signals. By acquiring modulo samples, the USF circumvents the clipping or saturation problem that is a fundamental bottleneck in conventional analog-to-digital converters (ADCs). In the context of the USF, several works have focused on bandlimited function classes and recently, a hardware validation of the modulo sampling approach has been presented. In a different direction, in this paper we focus on non-bandlimited function classes and consider the well-known super-resolution problem; we study the recovery of sparse signals (Dirac impulses) from low-pass filtered, modulo samples. Taking an end-to-end approach to USF based super-resolution, we present a novel recovery algorithm (US-SR) that leverages a doubly sparse structure of the modulo samples. We derive a sampling criterion for the US-SR method. A hardware experiment with the modulo ADC demonstrates the empirical robustness of our method in a realistic, noisy setting, thus validating its practical utility., Comment: 9 pages, 4 figures

Includes supplementary materials for the online appendix. Cognitive-relevant information is processed by different brain areas that cooperate to eventually produce a response. The relationship between local activity and global brain states during such processes, however, remains for the most part unexplored. To address this question, we designed a simple face-recognition task performed in patients with drug-resistant epilepsy and monitored with intracranial electroencephalography (EEG). Based on our observations, we developed a novel analytical framework (named “local–global” framework) to statistically correlate the brain activity in every recorded gray-matter region with the widespread connectivity fluctuations as proxy to identify concurrent local activations and global brain phenomena that may plausibly reflect a common functional network during cognition. The application of the local–global framework to the data from three subjects showed that similar connectivity fluctuations found across patients were mainly coupled to the local activity of brain areas involved in face information processing. In particular, our findings provide preliminary evidence that the reported global measures might be a novel signature of functional brain activity reorganization when a stimulus is processed in a task context regardless of the specific recorded areas. We thank all subjects for their participation in the study. We also thank Rodrigo Quian Quiroga and Hernán G. Rey for sharing some of their code to design the task paradigm. MVV was supported by a fellowship from “la Caixa” Foundation, Spain (ID 100010434, fellowship code LCF/BQ/DE17/11600022). MVV and ATC were supported by the Bial Foundation grant 106/18. GD, ATC and MVV were supported by the project “Clúster Emergent del Cervell Humà” (CECH, ref. 001-P-001682), within the framework of the European Research Development Fund Operational Program of Catalonia 2014–2020. ATC was supported by the Spanish National Research project (ref. PID2020-119072RA-I00/AEI/10.13039/501100011033) funded by the Spanish Ministry of Science, Innovation, and Universities (MCIU). GD was supported by a Spanish National Research project (ref. PID2019-105772GB-I00 MCIU AEI) funded by the Spanish Ministry of Science, Innovation, and Universities (MCIU), State Research Agency (AEI); HBP SGA3 Human Brain Project Specific Grant Agreement 3 (grant agreement no. 945539), funded by the EU H2020 FET Flagship programme; SGR Research Support Group support (ref. 2017 SGR 1545), funded by the Catalan Agency for Management of University and Research Grants (AGAUR); Neurotwin Digital twins for model-driven noninvasive electrical brain stimulation (grant agreement ID: 101017716) funded by the EU H2020 FET Proactive programme; euSNN European School of Network Neuroscience (grant agreement ID: 860563) funded by the EU H2020 MSCA-ITN Innovative Training Networks; Brain-Connects: Brain Connectivity during Stroke Recovery and Rehabilitation (ID 201725.33) funded by the Fundacio La Marato TV3; Corticity, FLAG-ERA JTC 2017 (ref. PCI2018-092891) funded by the Spanish Ministry of Science, Innovation and Universities (MCIU), State Research Agency (AEI). This research was also supported by “la Caixa” Foundation (CaixaImpulse Validate Program, project ref. CI20-00195).

Highlights • Fully automatic estimation of the peak frequency of the posterior dominant rhythm. • Automatic estimates are very similar to human ratings. • Algorithm made available with a simple graphical interface., Objective To develop and test a fully automated method for estimation of the peak frequency of the posterior dominant rhythm (PDR) in a large retrospective EEG cohort. Methods Thresholding was used to select suitable EEG data segments for spectral estimation for electrode O1 and O2. A random sample of 100 peak frequency estimates were blindly rated by two independent raters to validate the results of the automatic PDR peak frequency estimates. We investigated the relationship with age, sex and binary EEG classification. Results There were 9197 eligible EEGs which resulted in a total of 6104 PDR peak frequency estimates. The relationship between automatic estimates and age was found to be consistent with the literature. The correlation between human ratings and automatic scoring was very high, rho = 0.94–0.95. There was a sex difference of d = 0.33 emerging at puberty with females having a faster PDR peak frequency than males. Conclusions Fully automatic PDR peak frequency estimation not dependent on annotated EEG produced results that are very close to human ratings. Significance PDR peak frequency can be automatically estimated. A compiled version of the algorithm is included as an app for independent use.

This article studies the recovery of graphons when they are convolution kernels on compact (symmetric) metric spaces. This case is of particular interest since it covers the situation where the probability of an edge depends only on some unknown nonparametric function of the distance between latent points, referred to as Nonparametric Geometric Graphs (NGG). In this setting, adaptive estimation of NGG is possible using a spectral procedure combined with a Goldenshluger-Lepski adaptation method. The latent spaces covered by our framework encompass (among others) compact symmetric spaces of rank one, namely real spheres and projective spaces. For these latter, explicit computations of the eigen-basis and of the model complexity can be achieved, leading to quantitative non-asymptotic results. The time complexity of our method scales cubicly in the size of the graph and exponentially in the regularity of the graphon. Hence, this paper offers an algorithmically and theoretically efficient procedure to estimate smooth NGG. As a by product, this paper shows a non-asymptotic concentration result on the spectrum of integral operators defined by symmetric kernels (not necessarily positive)., Final version

The paper generalizes Thompson and Hilbert metric to the space of spectral densities. The resulting complete metric space has the differentiable structure of a Finsler manifold with explicit geodesics. The corresponding distances are filtering invariant, can be computed efficiently, and admit geodesic paths that preserve rationality; these are properties of fundamental importance in many engineering applications., ERC

The article proposes a method for the coefficients reconstruction of a discrete autocorrelation function of random signals with a unimodal power spectral density to construct their parametric models. The method is based on finding the optimal values of the relative width ΔFT and the weighting factor α in [0; 1] of the spectral mode, which characterizes the share of the Gaussian and resonant components in the spectrum envelope. The proposed method makes it possible to reduce by 1.5–4 times the discrepancy between the control and estimated spectra in comparison with the known approaches to parametric spectral analysis. An increase in the adequacy of spectral estimation makes it possible to reduce the length M of the analyzed time sample by a factor of 2.3–4 times, while maintaining the accuracy of the spectral analysis achieved by other known parametric methods. Winnings are achieved by using a priori information about the spectral properties of the analyzed process.

In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback-Leibler approximation of spectral densities, proposed by Pavon and Ferrante in [Pavon and Ferrante, 2006]. Our main result states that the algorithm globally converges to one of its fixed points., 16 pages, no figures. Corrected a few typos and changed title. To appear in IEEE Transactions on Automatic Control

This paper compares the skill of two algorithms that enable real-time estimation of the directional wave spectra exciting a ship from its measured motions. One algorithm consists of a nonlinear optimization of a parametric or non-parametric spectral model and the other is a Kalman filter based observer. Sea trials have been conducted on an oceanographic vessel that was instrumented with a six degree of freedom fiber optic gyro, complemented with a rate gyro, several accelerometers, a dedicated GPS receiver and a bow mounted down-looking wave radar with motion compensation. The two algorithms are applied to the measured data and a discussion is provided on their skill to recover the properties of existing sea states.

Introduction Various signal-processing techniques have been proposed to extract quantitative information about internal structures of tissues from the original radio frequency (RF) signals instead of an ultrasound image. The quantifiable parameter called the mean scatterer spacing (MSS) can be useful to detect changes in the quasi-periodic microstructure of tissues such as the liver or the spleen, using ultrasonic signals. Methods We evaluate and compare the performance of three classic methods of spectral estimation to calculate the MSS without operator intervention: Tufts-Kumaresan, SAC (Spectral Autocorrelation) and MUSIC (MUltiple SIgnal Classification). Initially the evaluations were performed with 10,000 signals simulated from a model in which the variables of interest are controlled, and then, real signals from sponge phantoms were used. Results For the simulated signals, the performance of all three methods decreased with increasing Ad or jitter levels. For the sponges, none of the methods accurately estimated the pore size. Conclusion For the simulated signals, Tufts-Kumaresan had the lowest performance, whereas SAC and MUSIC had similar results. For sponges, only Tufts-Kumaresan was able to detect the increase in the size of the pores of the sponge, although most often, it estimated sizes larger than expected.

This study examines a nonparametric inference on a stationary L\'evy-driven Ornstein-Uhlenbeck (OU) process $X = (X_{t})_{t \geq 0}$ with a compound Poisson subordinator. We propose a new spectral estimator for the L\'evy measure of the L\'evy-driven OU process $X$ under macroscopic observations. We also derive, for the estimator, multivariate central limit theorems over a finite number of design points, and high-dimensional central limit theorems in the case wherein the number of design points increases with an increase in the sample size. Built on these asymptotic results, we develop methods to construct confidence bands for the L\'evy measure and propose a practical method for bandwidth selection., Comment: 42 pages

Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods which rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both apriori knowledge of the number of sources, and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms, and when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of SNRs. Further, no performance sacrifice in simple scenarios is observed., Comment: 16 two-column pages, 12 figures, 1 table, Submitted for publication in IEEE Trans. Signal Processing

This paper focuses on suppressing spectral overlap for sub-band spectral estimation, with which we can greatly decrease the computational complexity of existing spectral estimation algorithms, such as nonlinear least squares spectral analysis and non-quadratic regularized sparse representation. Firstly, our study shows that the nominal ability of the high-order analysis filter to suppress spectral overlap is greatly weakened when filtering a finite-length sequence, because many meaningless zeros are used as samples in convolution operations. Next, an extrapolation-based filtering strategy is proposed to produce a series of estimates as the substitutions of the zeros and to recover the suppression ability. Meanwhile, a steady-state Kalman predictor is applied to perform a linearly-optimal extrapolation. Finally, several typical methods for spectral analysis are applied to demonstrate the effectiveness of the proposed strategy.

At the cost of added complexity and time, hyperspectral imaging provides a more accurate measure of the scene&rsquo, s irradiance compared to an RGB camera. Several camera designs with more than three channels have been proposed to improve the accuracy. The accuracy is often evaluated based on the estimation quality of the spectral data. Currently, such evaluations are carried out with either simulated data or color charts to relax the spatial registration requirement between the images. To overcome this limitation, this article presents an accurately registered image database of six icon paintings captured with five cameras with different number of channels, ranging from three (RGB) to more than a hundred (hyperspectral camera). Icons are challenging topics because they have complex surfaces that reflect light specularly with a high dynamic range. Two contributions are proposed to tackle this challenge. First, an imaging configuration is carefully arranged to control the specular reflection, confine the dynamic range, and provide a consistent signal-to-noise ratio for all the camera channels. Second, a multi-camera, feature-based registration method is proposed with an iterative outlier removal phase that improves the convergence and the accuracy of the process. The method was tested against three other approaches with different features or registration models.

We consider the problem of estimating the variance of the partial sums of a stationary time series that has either long memory, short memory, negative/intermediate memory, or is the first-difference of such a process. The rate of growth of this variance depends crucially on the type of memory, and we present results on the behavior of tapered sums of sample autocovariances in this context when the bandwidth vanishes asymptotically. We also present asymptotic results for the case that the bandwidth is a fixed proportion of sample size, extending known results to the case of flat-top tapers. We adopt the fixed proportion bandwidth perspective in our empirical section, presenting two methods for estimating the limiting critical values - both the subsampling method and a plug-in approach. Simulation studies compare the size and power of both approaches as applied to hypothesis testing for the mean. Both methods perform well-although the subsampling method appears to be better sized-and provide a viable framework for conducting inference for the mean. In summary, we supply a unified asymptotic theory that covers all different types of memory under a single umbrella. © 2013 Elsevier B.V. All rights reserved. 177 1 60 74 Cited By :4

Spectral estimation plays a significant role in engineering practice. Along with the spreading of sensor networks, more and more data are transmitted through unreliable channel which may lead to lost data. The most common method of spectral estimation uses FFT, but this needs the whole record without data loss. This paper presents a new FFT-based method for the problem which can be used at coherent sampling. The efficiency and accuracy is demonstrated via theoretical analysis, simulation and measurement results.

International audience; Wideband radars are promising systems that may provide numerous advantages, like simultaneous detection of slow and fast moving targets, high range-velocity resolution classification, and electronic countermeasures. Unfortunately, classical processing algorithms are challenged by the range-migration phenomenon that occurs then for fast moving targets. We propose a new approach where the range migration is used rather as an asset to retrieve information about target velocitiesand, subsequently, to obtain a velocity dealiased mode. More specifically three new complex spectral estimators are devised in case of a single low-PRF (pulse repetition frequency) wideband waveform. The new estimation schemes enable one to decrease the level of sidelobes that arise at ambiguous velocities and, thus, to enhance the discrimination capability of the radar. Synthetic data and experimental data are used to assess the performance of the proposed estimators.

The autocorrelation function is a commonly used tool in statistical time series analysis. Under the assumption of Gaussianity, the sample autocorrelation function is the standard method used to estimate this function given a finite number of observations. Non-Gaussian, impulsive observation noise following probability density functions with thick tails, which often occurs in practice, can bias this estimator, rendering classical time series analysis methods ineffective. This work examines the robustness of two estimators of correlation based on memoryless nonlinear functions of observations, the Phase-Phase Correlator (PPC) and the Median- of-Ratios Estimator (MRE), which are applicable to complex-valued Gaussian random pro- cesses. These estimators are very fast and easy to implement in current processors. We show that these estimators are robust from a bias perspective when complex-valued Gaussian pro- cesses are contaminated with impulsive noise at the expense of statistical efficiency at the assumed Gaussian distribution. Additionally, iterative versions of these estimators named the IMRE and IPPC are developed, realizing an improved bias performance over their non- iterative counterparts and the well-known robust Schweppe-type Generalized M-estimator utilizing a Huber cost function (SHGM). An impulsive noise suppression technique is developed using basis pursuit and a priori atom weighting derived from the newly developed iterative estimators. This new technique is proposed as an alternative to the robust filter cleaner, a Kalman filter-like approach that relies on linear prediction residuals to identity and replace corrupted observations. It does not have the same initialization issues as the robust filter cleaner. Robust spectral estimation methods are developed using these new estimators and impulsive noise suppression techniques. Results are obtained for synthetic complex-valued Guassian processes and real-world digital television signals collected using a software defined radio. Ph. D.

Time series displaying long-range correlations have been observed in numerous fields, such as biology, psychology, hydrology, and economics, among others. For rhythmic movements such as tapping tasks, the Wing–Kristofferson model offers a decomposition of the inter-response intervals based on a cognitive component and on a motor component. It has been suggested that the cognitive component should be modeled as a long- memory process and the motor component should be treated as a white noise process. Some probabilistic explanations for long-range dependences have been proposed, such as the aggregation of short-memory processes, the renewal-reward processes, and the error-duration processes. A new approach to the Wing–Kristofferson model which provides insights into the origin of long memory based on regime-switching processes is proposed. Under some assumptions, the autocorrelation function and the spectral density function of the model are obtained. Furthermore, an estimator of the parameters based on the maximization of the frequency-domain representation of the likelihood function is proposed. A simulation study evaluating the sample properties of this estimator is performed. Finally, an experimental study involving tapping tasks with two target frequencies is presented. info:eu-repo/semantics/publishedVersion

A interpretação da imagem ultrassônica, por ocorrer de modo visual e qualitativa, traz uma variação inter e intra-observador importante. A adoção de métodos quantitativos é uma forma de diminuir esta dependência. Entre tais métodos está a quantificação do espaçamento médio entre espalhadores (Mean Scatterer Spacing - MSS), que pode ser útil para detectar mudanças na microestrutura quasi-periódica de tecidos como o hepático ou o esplênico. Neste trabalho foram avaliados três métodos clássicos de estimação espectral para cálculo do MSS (sem intervenção do operador): BURG, WIENER e MUSIC. O intuito é comparar suas potencialidades para a estimação automática de espaçamento médio de espalhadores ultrassônicos. Inicialmente as avaliações foram realizadas com 10.000 sinais simulados a partir de um modelo em que se tem controle das variáveis de interesse, e em seguida foram utilizados sinais reais de phantoms de fios de nylon imersos em água. O método de BURG não conseguiu estimar adequadamente o espaçamento em sinais de phantom, tendo apresentado resultados equivalentes aos outros métodos deste trabalho somente para sinais simulados. O método de WIENER para os sinais simulados apresentou resultados de menor percentual de acerto, ficando em segundo lugar, para os sinais dos phantoms. O método de subespaço MUSIC apresentou melhor desempenho global em relação a BURG e WIENER, com resultados de 100% de acerto para o phantom de fio de nylon de 1,2 mm e 91,45% para 0,8 mm considerando uma janela de acerto de 10%. The interpretation of ultrasound imaging is essentially visual and qualitative, so there are important inter and intra-observer variations. Quantification methods aim at decreasing this dependency. Among those, the quantification of the Mean Scatterer Spacing (MSS) can be useful to detect changes in the microstructure of quasi-periodic tissues, such as liver or spleen. This study evaluated the following methods of spectral estimation for calculating the MSS (without requiring operator intervention): BURG, WIENER and MUSIC. The aim is to compare their potential for automatic estimation of MSS from ultrasonic scattering signals. Initially, the evaluation has been carried out using 10,000 simulated signals, with the aim of studying the behavior of the methods using a model in which the variables of interest can be controlled. Then, the methods have been applied to real signals of nylon phantoms immersed in water. The BURG method could not estimate the spacing of US phantom signals, presenting results similar to the other methods only for simulated signals. The WIENER method for the simulated signals was in second place in terms of percentage of success, when considering signals from the phantoms. The subspace method MUSIC had the best performance from all three methods.

Wereview spectral analysis and its application in inference for stationary processes. As can be seen from the list of references, the practice of spectral analysis is widespread in diverse scientific and engineering fields, particularly in signal processing and communications. One of the most striking characteristics of time series is their oscillatory behavior. This behavior is manifested, for example, in electroencephalogram (EEG) records, weekly sales, monthly environmental data, hourly financial indices, and in numerous economic data observed periodically in time. When observing such data the intuitive notion of periodicity is inescapable, and this led to the statistical problem of estimation of 'hidden periodicities' in time series. Schuster [47] was among the first who studied the problem seriously, and is credited with the invention of the so-called periodogram, a tool for discovering periodicities in oscillatory data. Consequently, spectral analysis and its ramification was further advanced by the pioneering works of Slutsky, Yule, Khintchine, Wiener, Cramer, Kolmogorov, Bartlett, Tukey, Parzen,Rosenblatt, Grenander, Koopmans, Brillinger, and Hannan. The goal of this communication is to introduce the reader to the topic of spectral analysis, and to review some state-of-the-art developments. It is of course not possible to give a full account of the literature on spectral analysis within this limited space. The selection of the references has been influenced by my own personal research interests . © 2010 John Wiley & Sons, Inc. 2 2 165 170

The paper investigates the relation between the parameters of an autoregressive moving average (ARMA) model and its equivalent moving average (EMA) model. On the basis of this relation, a new method is proposed for determining the ARMA model parameters from the coefficients of a finite-order EMA model. This method is a three-step approach: in the first step, a simple recursion relating the EMA model parameters and the cepstral coefficients of an ARMA process is derived to estimate the EMA model parameters; in the second step, the AR parameters are estimated by solving the linear equation set composed of EMA parameters; then, the MA parameters are obtained via simple computations using the estimated EMA and AR parameters. Simulations including both low- and high-order ARMA processes are given to demonstrate the performance of the new method. The end results are compared with the existing method in the literature over some performance criteria. It is observed from the simulations that our new algorithm produces the satisfactory and acceptable results. (C) 2006 Elsevier Inc. All rights reserved. C1 Pamukkale Univ, Dept Elect & Elect Engn, TR-20040 Kinikli, Denizli, Turkey. Tech Univ Istanbul, Elect & Commun Engn Dept, TR-34469 Istanbul, Turkey.

We consider the Georgiou-Lindquist constrained approximation of spectra in the Kullback-Leibler sense. We propose an alternative iterative algorithm to solve the corresponding convex optimization problem. The Lagrange multiplier is computed as a fixed point of a nonlinear matricial map. Simulation indicates that the algorithm is extremely effective.

International audience; S U M M A R Y It is often advantageous to investigate the relationship between two geophysical data sets in the spectral domain by calculating admittance and coherence functions. While there exist powerful Cartesian windowing techniques to estimate spatially localized (cross-)spectral properties, the inherent sphericity of planetary bodies sometimes necessitates an approach based in spherical coordinates. Direct localized spectral estimates on the sphere can be obtained by tapering, or multiplying the data by a suitable windowing function, and expanding the resultant field in spherical harmonics. The localization of a window in space and its spectral bandlimitation jointly determine the quality of the spatiospectral estimation. Two kinds of axisymmetric windows are here constructed that are ideally suited to this purpose: bandlimited functions that maximize their spatial energy within a cap of angular radius θ 0 , and spacelimited functions that maximize their spectral power within a spherical harmonic bandwidth L. Both concentration criteria yield an eigenvalue problem that is solved by an orthogonal family of data tapers, and the properties of these windows depend almost entirely upon the space-bandwidth product N 0 = (L + 1) θ 0 /π. The first N 0 − 1 windows are near perfectly concentrated, and the best-concentrated window approaches a lower bound imposed by a spherical uncertainty principle. In order to make robust localized estimates of the admittance and coherence spectra between two fields on the sphere, we propose a method analogous to Cartesian multitaper spectral analysis that uses our optimally concentrated data tapers. We show that the expectation of localized (cross-)power spectra calculated using our data tapers is nearly unbiased for stochastic processes when the input spectrum is white and when averages are made over all possible realizations of the random variables. In physical situations, only one realization of such a process will be available, but in this case, a weighted average of the spectra obtained using multiple data tapers well approximates the expected spectrum. While developed primarily to solve problems in planetary science, our method has applications in all areas of science that investigate spatiospectral relationships between data fields defined on a sphere.

In this paper we address the problem of devising and analyzing radar processors for space-time adaptive processing applications. We first define a class of adaptive filters based on the approximation of the overall disturbance with a multichannel autoregressive process. Thus we focus on a specific element of the family which exploits the modified square-root normalized maximum entropy algorithm for estimating the process coefficients. The performance assessment highlights the fast convergent capabilities of the novel processor, which for a limited number of training data, provides performances very close to the optimum filter. Finally we also devise and assess (both on simulated as well as on real radar data) two adaptive detectors which represent interesting solutions to deal with situations where a small number of training data is available. (C) 2004 Elsevier B.V. All rights reserved.

The Periodicallg Moving Part Modulation (PMPM) for the moving parts in target provides important signatures for target recognition. However, most radars operate in multiple target mode and can only get discontinuous clusters of the returned pulses, which makes it extremely difficult to extract PMPM signature from the echoes. This paper puts forward the Alternative Iteration Deconvolution based on Minimum Entropy criteria (AIDME) for spectral estimation of extended target's echoes, utilizing the special feature that the PMPM spectra usually have simple structures. Experimental results show that this method can effectively eliminate the severe influence caused by the convolution kernel and gain a satisfactory spectral estimation that approaches to the true spectrum.

Lag windows whose corresponding spectral windows are Jacobi polynomials or sums of Jacobi polynomials are introduced. The bias and variance of their spectral density estimators are investigated and their window bandwidth and characteristic exponent are determined.

We develop an efficient quantum implementation of an important signal processing algorithm for line spectral estimation: the matrix pencil method, which determines the frequencies and damping factors of signals consisting of finite sums of exponentially damped sinusoids. Our algorithm provides a quantum speedup in a natural regime where the sampling rate is much higher than the number of sinusoid components. Along the way, we develop techniques that are expected to be useful for other quantum algorithms as well—consecutive phase estimations to efficiently make products of asymmetric low rank matrices classically accessible and an alternative method to efficiently exponentiate non-Hermitian matrices. Our algorithm features an efficient quantum–classical division of labor: the time-critical steps are implemented in quantum superposition, while an interjacent step, requiring much fewer parameters, can operate classically. We show that frequencies and damping factors can be obtained in time logarithmic in the number of sampling points, exponentially faster than known classical algorithms., German Academic Scholarship Foundation, Fritz Haber Institute of the Max Planck Society, United States. Army Research Office, United States. Air Force. Office of Scientific Research

An efficient estimator is constructed for the quadratic covariation or integrated co-volatility matrix of a multivariate continuous martingale based on noisy and nonsynchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semi-parametric efficiency is established in the Cram\'{e}r-Rao sense. Main findings are that nonsynchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour., Comment: Published in at http://dx.doi.org/10.1214/14-AOS1224 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

TanDEM-X (TDX) forms with TerraSAR-X (TSX) the first single-pass synthetic aperture radar (SAR) interferometer in space with polarimetric capabilities. The availability of such system allows for the first time the acquisition and analysis of X-band Pol-InSAR data from space without the disturbing effect of temporal decorrelation. After two years of mission, time series with variable baseline over the same forest sites are available, allowing to (1) explore their information content, (2) assess penetration capabilities, (3) assess scattering model assumptions, and (4) estimate vertical structure and monitor its dynamics. This paper discusses for the first time the potential of estimating forest vertical structure from spaceborne single-pass interferometers, extending classical tomographic concepts. Results of first experiments with TSX/TDX multibaseline Pol-InSAR data acquired over the Tapajos national forest (Brazil) are shown. Especially regarding tropical forests, potentials and applications of X-band for forest structure monitoring will also be discussed.

Background: Complex fractionated atrial electrograms (CFAE) acquired during atrial fibrillation (AF) are commonly assessed using the discrete Fourier transform (DFT), but this can lead to inaccuracy. In this study, spectral estimators derived by averaging the autocorrelation function at lags were compared to the DFT. Method: Bipolar CFAE of at least 16 s duration were obtained from pulmonary vein ostia and left atrial free wall sites (9 paroxysmal and 10 persistent AF patients). Power spectra were computed using the DFT and three other methods: 1. a novel spectral estimator based on signal averaging (NSE), 2. the NSE with harmonic removal (NSH), and 3. the autocorrelation function average at lags (AFA). Three spectral parameters were calculated: 1. the largest fundamental spectral peak, known as the dominant frequency (DF), 2. the DF amplitude (DA), and 3. the mean spectral profile (MP), which quantifies noise floor level. For each spectral estimator and parameter, the significance of the difference between paroxysmal and persistent AF was determined. Results: For all estimators, mean DA and mean DF values were higher in persistent AF, while the mean MP value was higher in paroxysmal AF. The differences in means between paroxysmals and persistents were highly significant for 3/3 NSE and NSH measurements and for 2/3 DFT and AFA measurements (p

An efficient estimator is constructed for the quadratic covariation or integrated covolatility matrix of a multivariate continuous martingale based on noisy and non-synchronous observations under high-frequency asymptotics. Our approach relies on an asymptotically equivalent continuous-time observation model where a local generalised method of moments in the spectral domain turns out to be optimal. Asymptotic semiparametric efficiency is established in the Cramér-Rao sense. Main findings are that non-synchronicity of observation times has no impact on the asymptotics and that major efficiency gains are possible under correlation. Simulations illustrate the finite-sample behaviour.

This article describes identification of vibration frequencies in a spacecraft. A mathematical model of a simple spacecraft is built in MATLAG code, and after a theoretical overview, this spacecraft model is simulated, using a torque excitation, to generate time series measurements. These measurements are subsequently used in the identification experiments. Parametric methods, here represented by AR, ARX, ARMA and ARMAX, are the main concern, but nonparametric methods are also discussed."

Forest characterization and biomass estimation by means of remote sensing systems are nowadays “hot topics” within the remote sensing community, given their importance in the terrestrial carbon budget. In fact, forest vertical structure is a key variable for assessing biodiversity and structural degradation and/or regeneration. Moreover, the (vertical) structure information is important as it can allow the development of accurate and robust (alometric) estimators of the forest biomass. In this paper, potentials and challenges of forest vertical structure estimation with low frequency multibaseline polarimetric synthetic aperture radar are reviewed and discussed.

The generalised autocovariance function is defined for a stationary stochastic process as the inverse Fourier transform of the power transformation of the spectral density function. Depending on the value of the transformation parameter, this function nests the inverse and the traditional autocovariance functions. A frequency domain non-parametric estimator based on the power transformation of the pooled periodogram is considered and its asymptotic distribution is derived. The results are employed to construct classes of tests of the white noise hypothesis, for clustering and discrimination of stochastic processes and to introduce a novel feature matching estimator of the spectrum.

Background The dominant frequency of the Fourier power spectrum is useful to analyze complex fractionated atrial electrograms (CFAE), but spectral resolution is limited and uniform from DC to the Nyquist frequency. Herein the spectral resolution of a recently described and relatively new spectral estimation technique is compared to the Fourier radix-2 implementation. Methods In 10 paroxysmal and 10 persistent atrial fibrillation patients, 216 CFAE were acquired from the pulmonary vein ostia and left atrial free wall (977 Hz sampling rate, 8192 sample points, 8.4 s duration). With these parameter values, in the physiologic range of 3–10 Hz, two frequency components can theoretically be resolved at 0.24 Hz using Fourier analysis and at 0.10 Hz on average using the new technique. For testing, two closely-spaced periodic components were synthesized from two different CFAE recordings, and combined with two other CFAE recordings magnified 2×, that served as interference signals. The ability to resolve synthesized frequency components in the range 3–4 Hz, 4–5 Hz, …, 9–10 Hz was determined for 15 trials each (105 total). Results With the added interference, frequency resolution averaged 0.29 ± 0.22 Hz for Fourier versus 0.16 ± 0.10 Hz for the new method (p p Conclusions Within the physiologically relevant frequency range for characterization of CFAE, the new method has approximately twice the spectral resolution of Fourier analysis, there is less error in estimating frequencies, and peaks appear more readily above the noise floor. Theoretically, when interference is not present, to resolve frequency components separated by 0.10 Hz using Fourier analysis would require an 18.2 s sequence duration, versus 8.4 s with the new method.

Spectral velocity estimation is considered the gold standard in medical ultrasound. Peak systole (PS), end diastole (ED), and resistive index (RI) are used clinically. Angle correction is performed using a flow angle set manually. With Transverse Oscillation (TO) velocity estimates the flow angle, peak systole (PSTO), end diastole (EDTO), and resistive index (RITO) are estimated. This study investigates if these clinical parameters are estimated equally good using spectral and TO data. The right common carotid arteries of three healthy volunteers were scanned longitudinally. Average TO flow angles and std were calculated { 52±18 ; 55±23 ; 60±16 }°. Spectral angles { 52 ; 56 ; 52 }° were obtained from the B-mode images. Obtained values are: PSTO { 76±15 ; 89±28 ; 77±7 } cm/s, spectral PS { 77 ; 110 ; 76 } cm/s, EDTO { 10±3 ; 14±8 ; 15±3 } cm/s, spectral ED { 18 ; 13 ; 20 } cm/s, RITO { 0.87±0.05 ; 0.79±0.21 ; 0.79±0.06 }, and spectral RI { 0.77 ; 0.88 ; 0.73 }. Vector angles are within ±two std of the spectral angle. TO velocity estimates are within ±three std of the spectral estimates. RITO are within ±two std of the spectral estimates. Preliminary data indicates that the TO and spectral velocity estimates are equally good. With TO there is no manual angle setting and no flow angle limitation. TO velocity estimation can also automatically handle situations where the angle varies over the cardiac cycle. More detailed temporal and spatial vector estimates with diagnostic potential are available with the TO velocity estimation.© (2011) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

We revisit the topics of near-field adaptive beamforming and source localization following an alternative approach based on a spatio- temporal spectral representation of the acoustic wave field. With the proposed method, the wave field is expressed as a separable combination of the signal and spatial components that characterize the various sources in the acoustic scene. This allows beamform- ing operations such as beam steering and sidelobe canceling to be translated into a two-dimensional (2D) sampling problem, where the sampling kernels are derived according to a parametric model repre- senting the 2D spectral pattern generated in the presence of a source. Conversely, the spectral pattern can be estimated from an arbitrary input through the use of parametric spectral estimation techniques, providing a novel solution to the near-field source localization prob- lem.

In this paper, we first describe a matricial Newton-type algorithm designed to solve the multivariable spectrum approximation problem. We then prove its global convergence. Finally, we apply this approximation procedure to multivariate spectral estimation, and test its effectiveness through simulation. Simulation shows that, in the case of short observation records, this method may provide a valid alternative to standard multivariable identification techniques such as Matlab's PEM and Matlab's N4SID.

Signal parameter estimation in the presence of noise has been a key area of research. Many applications have benefited from advancements made in this field within the last two decades. The method proposed in the thesis introduces a new family of infinite impulse response adaptive notch filters that forms multiple notches using a second-order factorization of an all-pass transfer function. The filter sections are orthogonal to each other. The resulting notch filter requires few parameters, facilitates the formation of the desired band rejection filter response, and also leads to various useful implementations (Cascaded, Parallel, Using Filter banks). In this thesis a variation of cascade type structure is used. The algorithm proposed for adaptively estimating filter coefficients is based on WRLS method. Fast convergence along with lower bias as compared to previous algorithms is achieved. This property is particularly attractive for detection and tracking of unknown sinusoids. Computer simulations are provided to illustrate the performance of the proposed adaptive notch filters in terms of bias, speed of convergence, and tracking capability. Also simulations for detection of multiband signals is given.

A new class of large-sample covariance and spectral density matrix estimators is proposed based on the notion of flat-top kernels. The new estimators are shown to be higher-order accurate when higher-order accuracy is possible. A discussion on kernel choice is presented as well as a supporting finite-sample simulation. The problem of spectral estimation under a potential lack of finite fourth moments is also addressed. The higher-order accuracy of flat-top kernel estimators typically comes at the sacrifice of the positive semidefinite property. Nevertheless, we show how a flat-top estimator can be modified to become positive semidefinite (even strictly positive definite) while maintaining its higher-order accuracy. In addition, an easy (and consistent) procedure for optimal bandwidth choice is given this procedure estimates the optimal bandwidth associated with each individual element of the target matrix, automatically sensing (and adapting to) the underlying correlation structure. 1 42 Cited By :23 Article in Press

In this paper, we consider the problem of bandwidth choice in the parallel settings of nonparametric kernel smoothed spectra] density and probability density estimation. We propose a new class of 'plug-in' type bandwidth estimators, and show their favorable asymptotic properties. The new estimators automatically adapt to the degree of underlying smoothness which is unknown. The main idea behind the new estimators is the use of infinite-order 'flat-top' kernels for estimation of the constants implicit in the formulas giving the asymptotically optimal bandwidth choices. The proposed bandwidth choice rule for 'flat-top' kernels has a direct analogy with the notion of thresholding in wavelets. It is shown that the use of infinite-order kernels in the pilot estimator has a twofold advantage: (a) accurate estimation of the bandwidth constants, and (b) easy determination of the required 'pilot' kernel bandwidth. 15 4-5 517 533 Cited By :39

A technique to analyze short-period (

Analysis of variance type models are considered for a regression function or for the logarithm of a probability function, conditional probability function, density function, conditional density function, hazard function, conditional hazard function or spectral density function. Polynomial splines are used to model the main effects, and their tensor products are used to model any interaction components that are included. In the special context of survival analysis, the baseline hazard function is modeled and nonproportionality is allowed. In general, the theory involves the $L_2$ rate of convergence for the fitted model and its components. The methodology involves least squares and maximum likelihood estimation, stepwise addition of basis functions using Rao statistics, stepwise deletion using Wald statistics and model selection using the Bayesian information criterion, cross-validation or an independent test set. Publicly available software, written in C and interfaced to S/S-PLUS, is used to apply this methodology to real data.

There are many practical applications of lattice form recursive linear least square algorithms (called lattices for short) in signal processing, communications, and control systems. The goal of this tutorial is to help practicing engineers to decide if lattices are appropriate for their particular projects.