Random time-series model identification from binary-valued observations and quantized measurements

A coprime sensor array (CSA) is a sparse array geometry that interleaves two spatially undersampled uniform linear arrays (ULAs) with coprime undersampling factors. The CSA spans the same aperture and has equivalent resolution as a fully populated ULA, but uses fewer sensors. Previous works have introduced three CSA processors as spatial power spectral density (PSD) estimators: the Product, Min, and Blend processors. However, two of these processors display increased PSD esti-mate variance over the ULA PSD estimate. This dissertation focuses on reducing the variance of the CSA PSD estimators. PSD estimation traditionally relies on averag-ing uncorrelated coherent measurements (snapshots) to reduce variance. However,non-stationary underwater sonar environments often preclude increasing the num-ber of snapshots required to achieve a desirable PSD variance. In the traditional signal processing literature, there are two alternative methods to reduce variance without additional snapshot cost. The multitaper (MT) method and Welch's over-lapping segment averaging (WOSA) method improve PSD variance by O(K) at the expense of an O(K) resolution decrease by averaging K uncorrelated PSD estimates. Multitaper obtains these uncorrelated estimates by windowing the array with K or-thogonal tapers that span the entire array aperture. In contrast, WOSA obtains the uncorrelated estimates by subdividing the array into K possibly overlapping segments.This dissertation extends these two existing ULA variance reduction techniques to the CSA processors, making four main contributions. The first proposes the multitapered Product processor (MT-Product) that estimates the spatial PSD with reduced variance with respect to the traditional CSA Product processor but still uses fewer sensors than a fully populated ULA. The second proposes the multita-pered Min processor (MT-Min) that reduces the PSD estimate variance further than either MT-Product or Product. The MT-Min estimator has variance comparable to a multitapered ULA. The third proposes the multitapered Blend processor (MT-Blend) that blends MT-Product's attenuation of multiple source cross-terms with MT-Min's low variance while still achieving an O(K) variance reduction over the traditional Blend processor. The final contribution proposes the Welch overlapping segment averaging Product processor (WOSA-Product) that estimates the spatial PSD with reduced variance with respect to the traditional CSA Product processor but still uses fewer sensors than a fully populated ULA. WOSA-Product is gener-ally able to form a larger number of uncorrelated PSD estimates than MT-Product. Closed-form statistics for spatially white Gaussian processes are derived for MT-Product, MT-Min, and WOSA-Product. Simulations verify the variance reduction predicted by the analytical derivations each processor, and the effects of WOSA-Product segment length on resolution, variance reduction, and peak sidelobe levels are discussed.

Simulation of non-Gaussian surfaces with FFT

Spectrum analysis is one of the momentous fields in signal processing. It has a large variety of applications in radar, sonar, speech and image processing. Parametric methods have been proposed and employed for spectrum analysis including power spectral density (PSD) estimation. These methods estimate the parameters of a statistical model and compute the PSD, afterwards. In some circumstances one is obliged to deal with observations of numerous geographically dispersed sensors, to either increase the precision or based on application demands. Having a set of sensors linked together to take the advantages of cooperation and network topology, one obtains a more comprehensive estimation. In this chapter, the authors propose and study four different algorithms capable of facing spatio-temporal variations for parametric modeling and PSD estimation using wireless sensor networks (WSNs). For this purpose, the authors first validate the proposed algorithms using theoretical and mathematical formulations. Thereafter, performing simulation tasks demonstrates and supports the theoretical achievements. The next section of the chapter illustrates the concepts to a greater degree, the authors analyze and compare the performance of these algorithms with each other, as well as with the simple PSD estimation using individual sensors, wherein there is no cooperation among the nodes.

The aim of this study was to assess whether power spectrum estimates of electroencephalogram (EEG) can be used as a biomarker for autism spectrum disorder (ASD). EEG collected from ASD and control participants performing a short-memory task was preprocessed to remove noise and artefacts, power spectral density (PSD) estimates were obtained by the modified covariance method and used as the study features that were subjected next to the Kruskal-Wallis analysis of differences. After verifying that the features (PSD estimates) were statistically different between the autistic and control subjects, these PSD estimates were classified using the 'k nearest neighbour' (KNN) classification algorithm with the average accuracy of 89.29%. This result indicates that EEG of autistic and control individuals may contain statistically different features; therefore, EEG power spectrum may be used as a biomarker for autism.

Eighty-one prescription drugs were divided into three groups according to the strength of the auto-correlation (strong, weak or none) of daily variations in the drug supply amounts at a pharmacy. The power spectral density and auto-correlation function were used as an indicator for the classification. Sixty-four drugs fell into the no auto-correlation group, 15 drugs into the weak auto-correlation group and 2 drugs into the strong auto-correlation group. Interestingly, our grouping using auto-correlation as a criterion was consistent with the target-oriented classification (standard commodity classification of Japan).

Choice of ultra wideband (UWB) pulse shapes has become an interesting challenge such that the spectral limits of the frequency band approved by the Federal Communications Commission (FCC) can be utilised efficiently. In this paper, we compare the efficiency of various UWB pulse shapes based upon their power spectral density (PSD) and autocorrelation functions (ACF). We propose a set of prolate spheroidal wave functions (PSWF) for a typical M-ary pulse shape modulation (PSM) scheme. In the process, we show closed form expressions for the ACF of PSWF-based UWB pulse shapes of different orders.

Signal processing of flutter flight test data enables verification of aircraft flutter design, and the signal from a flutter flight test excited by atmospheric turbulence is a particularly important form of the flutter test. Owing to the randomness of atmospheric turbulence excitation, multi-channel analysis of turbulence responses at various positions in the same component can improve the analytical accuracy of flutter signal processing. The relationship between the maximum singular value of the multi-channel turbulence response power spectral density matrix and the system self-power spectral density function is elucidated herein using a frequency domain decomposition method. However, there is a contradiction in the power spectral density function between the spectral line density and the spectral line smoothing calculated based on the periodogram of the frequency domain decomposition. By applying an autoregressive spectral model, the power spectral density function of the turbulence response is calculated to achieve spectral line smoothing and sufficient spectral line density. Additionally, the power spectral density function is then used to construct the power spectral density function matrix of the multi-channel turbulence response, and the maximum singular value curve is calculated based on the singular value decomposition of each spectral pin. Finally, the modal parameters of the turbulence response signal are estimated via multi-modal frequency domain fitting. The developed approach is validated based on simulations and flutter flight test turbulence response signals.

Many well-known and frequently employed Bayesian clean speech estimators have been derived under the assumption that the true power spectral densities (PSDs) of speech and noise are exactly known. In practice, however, only power spectral density (PSD) estimates are available. Simply neglecting PSD estimation errors and handling the estimates as true values leads to speech estimation errors causing musical noise and undesired suppression of speech. In this paper, the uncertainty of the available speech PSD estimates is addressed. The main contributions are the following. First, we summarize and examine ways to model and incorporate the uncertainty of PSD estimates for a more robust speech enhancement performance. Second, a novel nonlinear clean speech estimator is derived that takes into account prior knowledge about the absolute value of typical speech PSDs. Third, we show that the derived statistical framework provides uncertainty-aware counterparts to a number of well-known conventional clean speech estimators such as the Wiener filter and Ephraim and Malah's amplitude estimators. Fourth, we show how modern PSD estimators can be incorporated into the theoretical framework and propose to employ frequency dependent priors. Finally, the effects and benefits of considering the uncertainty of speech PSD estimates are analyzed, discussed, and evaluated via instrumental measures and a listening experiment.

ABSTRACTA radio frequency interference (RFI) excision algorithm based on spectral kurtosis, a spectral variant of time‐domain kurtosis, is proposed and implemented in software. The algorithm works by providing a robust estimator for Gaussian noise that, when violated, indicates the presence of non‐Gaussian RFI. A theoretical formalism is used that unifies the well‐known time‐domain kurtosis estimator with past work related to spectral kurtosis, and leads naturally to a single expression encompassing both. The algorithm accumulates the first two powers of M power spectral density (PSD) estimates, obtained via Fourier transform, to form a spectral kurtosis (SK) estimator whose expected statistical variance is used to define an RFI detection threshold. The performance of the algorithm is theoretically evaluated for different time‐domain RFI characteristics and signal‐to‐noise ratios η. The theoretical performance of the algorithm for intermittent RFI (RFI present in R out of M PSD estimates) is evaluated and shown to depend greatly on the duty cycle, d = R/M. The algorithm is most effective for d = 1/(4 + η), but cannot distinguish RFI from Gaussian noise at any η when d = 0.5. The expected efficiency and robustness of the algorithm are tested using data from the newly designed FASR Subsystem Testbed radio interferometer operating at the Owens Valley Solar Array. The ability of the algorithm to discriminate RFI against the temporally and spectrally complex radio emission produced during solar radio bursts is demonstrated.

Reduction of leakage and increase of resolution in power spectral density and coherence functions

In seismic engineering, the earthquake-induced ground motion is generally represented in the form of pseudo-acceleration or displacement response spectra. There are, however, situations in which the response spectrum is not considered appropriate, and a fully dynamic analysis is required. In this case, the most effective approach is to define artificial spectrum-compatible stationary accelerograms, which are generated to match the target elastic response spectrum. So a Power Spectral Density (PSD) function is derived from the response spectrum. However, the above approach possesses the drawback that the artificial accelerograms do not manifest the variability in time and in frequency observed from the analysis of real earthquakes. Indeed, the recorded accelerograms can be considered sample of a fully non-stationary process. In this study a procedure based on the analysis of a set of accelerograms recorded in a chosen site to take into account their time and frequency variability is described. In particular the generation of artificial fully non-stationary accelerograms is performed in three steps. In the first step the spectrum-compatible PSD function, in the hypothesis of stationary excitations, is derived. In the second step the spectrum-compatible Evolutionary Power Spectral Density (EPSD) function is obtained by an iterative procedure to improve the match with the target response spectrum starting from the PSD function, once a time-frequency modulating function is chosen. In the third step the artificial accelerograms are generated by the well-known Shinozuka and Jan (J Sound Vib 25:111–128, 1972) formula and deterministic analyses can be performed to evaluate the structural response. Once the EPSD spectrum-compatible function is derived, a method recently proposed by the authors (Muscolino and Alderucci in Probab Eng Mech 40:75–89, 2015), is adopted to evaluate the EPSD response function of linear structural systems subjected to fully non-stationary excitations by very handy explicit closed-form.

A new method for the generation of a correlated pseudo-random gaussian process with a desired power spectral density or auto-correlation function is presented. Samples of the pseudo-random process are generated at the output of the cascade connection of a pseudo-random number (PN) generator and correlation-shaping finite impulse response filter. The proposed method generates a pseudo-random gaussian process, having arbitrary correlation properties, with a high degree of accuracy. Computer simulation examples are given to demonstrate the performance of the method.

Three power spectral density estimation problems are considered in this presentation. These are the estimation of power spectral density for a single scalar time series (or equivalently a line array), estimation of power spectral density matrices for vector valued time series, and the estimation of wavenumber or frequency-wavenumber spectra for random fields. The paper is primarily a tutorial coverage of autoregressive (also called maximum entropy) and maximum likelihood methods of spectral analysis. In addition to standard material on these subjects a recent generalization of the Burg algorithm from scalar to vector time series is included.

In the study of human cognitive activity using electroencephalogram (EEG), the brain dynamics parameters and characteristics play a crucial role. They allow to investigate the changes in functionality depending on the environment and task performance process, and also to access the intensity of the brain activity in various locations of the cortex and its dependencies. Usually, the dynamics of activation of different brain areas during the cognitive tasks are being studied by spectral analysis based on power spectral density (PSD) estimation, and coherence analysis, which are de facto standard tools in quantitative characterization of brain activity. PSD and coherence reflect the strength of oscillations and similarity of the emergence of these oscillations in the brain, respectively, while the concept of stability of brain activity over time is not well defined and less formalized. We propose to employ the detrended fluctuation analysis (DFA) as a measure of the EEG persistence over time, and use the DFA scaling exponent as its quantitative characteristics. We applied DFA to the study of the changes in activation in brain dynamics during mental calculations and united it with PSD and coherence estimation. In the experiment, EEGs during resting state and mental serial subtraction from 36 subjects were recorded and analyzed in four frequency ranges: θ1 (4.1–5.8 Hz), θ2 (5.9–7.4 Hz), β1 (13–19.9 Hz), and β2 (20–25 Hz). PSD maps to access the intensity of cortex activation and coherence to quantify the connections between different brain areas were calculated, the distribution of DFA scaling exponent over the head surface was exploited to measure the time characteristics of the dynamics of brain activity. Obtained arrangements of DFA scaling exponent suggest that normal functioning of the brain is characterized by long-term temporal correlations in the cortex. Topographical distribution of the DFA scaling exponent was comparable for θ and β frequency bands, demonstrating the largest values of DFA scaling exponent during cognitive activation. The study shows that the long-term temporal correlations evaluated by DFA can be of great interest for diagnosis of the variety of brain dysfunctions of different etiology in the future.

In order to simulate the non-Gaussian fluctuating wind pressure with prescribed lower-order moments and its target power spectral density (PSD) function, the following framework is proposed in the present paper: Firstly, the PSD function of fluctuating wind pressure is deduced rigorously according to the relationship between the wind pressure and velocity; Then, an efficient yet practical method by which the fluctuating wind pressure may be reproduced with the designated skewness and kurtosis is presented based on the derived PSD function, Johnson translator system, and digital filter; Finally, in order to corroborate the feasibility and correctness of the present methodology, a numerical example of simulating one-dimensional univariate non-Gaussian fluctuating wind pressure is taken into consideration. Numerical results indicate that the statistical parameters, such as the skewness and kurtosis, of the simulated fluctuating wind pressure are in remarkably agreement with their targets. Likewise, the PSDs of the simulated records and target show considerably good agreement with each other.