Multitaper Estimation of the Coherence Spectrum in low SNR

A pseudo coherence estimate using multitapers is presented. The estimate has better localization for sinusoids and is shown to have lower variance for disturbances compared to the usual coherence estimator. This makes it superior in terms of finding coherent frequencies between two sinusoidal signals; even when observed in low SNR. Different sets of multitapers are investigated and the weights of the final coherence estimate are adjusted for a low-biased estimate of a single sinusoid. The proposed method is more computationally efficient than data dependent methods, and does still give comparable results

Analysis of Dynamic Brain Imaging Data

Modern imaging techniques for probing brain function, including functional Magnetic Resonance Imaging, intrinsic and extrinsic contrast optical imaging, and magnetoencephalography, generate large data sets with complex content. In this paper we develop appropriate techniques of analysis and visualization of such imaging data, in order to separate the signal from the noise, as well as to characterize the signal. The techniques developed fall into the general category of multivariate time series analysis, and in particular we extensively use the multitaper framework of spectral analysis. We develop specific protocols for the analysis of fMRI, optical imaging and MEG data, and illustrate the techniques by applications to real data sets generated by these imaging modalities. In general, the analysis protocols involve two distinct stages: `noise' characterization and suppression, and `signal' characterization and visualization. An important general conclusion of our study is the utility of a frequency-based representation, with short, moving analysis windows to account for non-stationarity in the data. Of particular note are (a) the development of a decomposition technique (`space-frequency singular value decomposition') that is shown to be a useful means of characterizing the image data, and (b) the development of an algorithm, based on multitaper methods, for the removal of approximately periodic physiological artifacts arising from cardiac and respiratory sources.Comment: 40 pages; 26 figures with subparts including 3 figures as .gif files. Originally submitted to the neuro-sys archive which was never publicly announced (was 9804003

A Multitaper-Random Demodulator Model for Narrowband Compressive Spectral Estimation

The random demodulator (RD) is a compressive sensing (CS) system for acquiring and recovering bandlimited sparse signals, which are approximated by multi-tones. Signal recovery employs the discrete Fourier transform based periodogram, though due to bias and variance constraints, it is an inconsistent spectral estimator. This paper presents a Multitaper RD (MT-RD) architecture for compressive spectrum estimation, which exploits the inherent advantage of the MT spectral estimation method from the spectral leakage perspective. Experimental results for sparse, narrowband signals corroborate that the MT-RD model enhances sparsity so affording superior CS performance compared with the original RD system in terms of both lower power spectrum leakage and improved input noise robustness

Tracking aftershock sequences using empirical matched field processing

Extensive aftershock sequences present a significant problem to seismological data centres attempting to produce near real-time comprehensive seismic event bulletins. An elevated number of events to process and poorer performance of automatic phase association algorithms can lead to large delays in processing and a greatly increased human workload. Global monitoring is often performed using seismic array stations at considerable distances from the events involved. Empirical matched field processing (EMFP) is a narrow-frequency band array signal processing technique that recognizes the inter-sensor phase and amplitude relations associated with wavefronts approaching a sensor array from a given direction. We demonstrate that EMFP, using a template obtained from the first P arrival from the main shock alone, can efficiently detect and identify P arrivals on that array from subsequent events in the aftershock zone with exceptionally few false alarms (signals from other sources). The empirical wavefield template encodes all the narrow-band phase and amplitude relations observed for the main shock signal. These relations are also often robust and repeatable characteristics of signals from nearby events. The EMFP detection statistic compares the phase and amplitude relations at a given time in the incoming data stream with those for the template and is sensitive to very short-duration signals with the required characteristics. Significant deviations from the plane-wavefront model that typically degrade the performance of standard beamforming techniques can enhance signal characterization using EMFP. Waveform correlation techniques typically perform poorly for aftershocks from large earthquakes due to the distances between hypocentres and the wide range of event magnitudes and source mechanisms. EMFP on remote seismic arrays mitigates these difficulties; the narrow-band nature of the procedure makes arrival identification less sensitive to the signals’ temporal form and spectral content. The empirical steering vectors derived for the main shock P arrival can reduce the frequency dependency of the slowness vector estimates. This property helps us to automatically screen out arrivals from outside of the aftershock zone. Standard array processing pipelines could be enhanced by including both plane-wave and empirical matched field steering vectors. This would maintain present capability for the plane-wave steering vectors and provide increased sensitivity and resolution for those sources for which we have empirical calibrations.Tracking aftershock sequences using empirical matched field processingacceptedVersio

A characterization of periodicity in the voltage time series of a riometer

Author Posting. © American Geophysical Union, 2020. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research: Space Physics 125(7), (2020): e2019JA027160, doi:10.1029/2019JA027160.This paper reveals unprecedented periodicity in the voltage series of relative ionospheric opacity meters (riometers) of the Canadian Riometer Array (CRA). In quiet times, the riometer voltage series is accurately modeled by a stochastic process whose components include both a six term expansion in harmonic functions and some amplitude modulated modes of lower signal to noise ratio (SNR). In units of cycles per sidereal day (cpsd), the frequencies of the six harmonic functions lie within 0.01 cpsd of an integer. Earth's rotation induces a splitting of the low SNR components, resulting in the appearance of nine multiplets in standardized power spectrum estimates of the considered CRA voltage series. A second feature of these spectrum estimates is a 6 min periodic element appearing in both the CRA voltage series and the proton mass density series of the Advanced Composition Explorer (ACE). Spectral peak frequencies have been detected, which lie near established solar mode frequency estimates. In addition, some of these peak frequency estimates are coincident with peak frequency estimates of the standardized power spectra for the time series of proton mass density and interplanetary magnetic field strength (IMF) at ACE.“Marshall_Francois_Supporting_Information_JGR_2019.pdf” contains a summary of the supporting information. The 1 hr sampled F10.7 series was obtained from DRAO (National Research Council, 2017). The three MAG time series of IMF strength were acquired from The ACE Science Center (2007), while the SWEPAM time series of proton mass density was acquired from Space Weather Prediction Center, National Oceanic and Atmospheric Administration (2018). The relevant data sets for the analysis of this paper are included in Marshall (2019). This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC), Canadian Statistical Sciences Institute (CANSSI), Bonneyville Power Authority, and Queen's University. David J. Thomson, the official holder of the grants and contracts, provided research and conference funding to advance this project. Special thanks to Ken F. Tapping (DRAO of NRCan) for his guidance in finding the data sets relevant to solar radio emissions. Glen Takahara, of the Department of Mathematics and Statistics at Queen's University, suggested exploring different data sets to confirm the modal origin of spectral peaks observed in the Ottawa riometer of the CRA. Alessandra A. Pacini of the Arecibo Observatory recommended checking to see if some of the modes could have been driven by the harmonics of Earth's rotation. Frank Vernon of the Institute of Geophysics and Planetary Physics at Scripps Institution of Oceanography confirmed how seismic data could be expected to reveal coincident spectral peaks at the detected frequencies in the riometer standardized spectra.2020-10-2

Deteção espetral de banda larga para rádio cógnitivo

Doutoramento em TelecomunicaçõesEsta tese tem como objetivo o desenvolvimento de uma unidade autónoma de deteção espetral em tempo real. Para tal são analisadas várias implementações para a estimação do nível de ruído de fundo de forma a se poder criar um limiar adaptativo para um detetor com uma taxa constante de falso alarme. Além da identificação binária da utilização do espetro, pretende-se também obter a classificação individual de cada transmissor e a sua ocupação ao longo do tempo. Para tal são exploradas duas soluções baseadas no algoritmo, de agrupamento de dados, conhecido como maximização de expectativas que permite identificar os sinais analisados pela potência recebida e relação de fase entre dois recetores. Um algoritmo de deteção de sinal baseado também na relação de fase de dois recetores e sem necessidade de estimação do ruído de fundo é também demonstrado. Este algoritmo foi otimizado para permitir uma implementação eficiente num arranjo de portas programáveis em campo a funcionar em tempo real para uma elevada largura de banda, permitindo também estimar a direção da transmissão detetada.The purpose of this thesis is to develop an autonomous unit for real time spectrum sensing. For this purpose, several implementations for the estimation of the background noise level are analysed to create an adaptive threshold and ensure a constant false alarm rate detector. In addition to the binary identification of the spectrum usage, it is also intended to obtain an individual classification of each transmitter occupation and its spectrum usage over time. To do so, two solutions based on the expectation maximization data clustering, that allow to identify the analyzed signals by the received power and phase relation between two receivers, were explored. A signal detection algorithm, also based on the phase relationship between two receivers and with no need for noise estimation is also demonstrated. This algorithm has been optimized to allow an efficient implementation in a FPGA operating in real time for a high bandwidth and it also allows the estimation of the direction of arrival of the detected transmission

Non-identical smoothing operators for estimating time-frequency interdependence in electrophysiological recordings

Synchronization of neural activity from distant parts of the brain is crucial for the coordination of cognitive activities. Because neural synchronization varies both in time and frequency, time–frequency (T-F) coherence is commonly employed to assess interdependences in electrophysiological recordings. T-F coherence entails smoothing the cross and power spectra to ensure statistical consistency of the estimate, which reduces its T-F resolution. This trade-off has been described in detail when the cross and power spectra are smoothed using identical smoothing operators, which may yield spurious coherent frequencies. In this article, we examine the use of non-identical smoothing operators for the estimation of T-F interdependence, i.e., phase synchronization is characterized by phase locking between signals captured by the cross spectrum and we may hence improve the trade-off by selectively smoothing the auto spectra. We first show that the frequency marginal density of the present estimate is bound within [0,1] when using non-identical smoothing operators. An analytic calculation of the bias and variance of present estimators is performed and compared with the bias and variance of standard T-F coherence using Monte Carlo simulations. We then test the use of non-identical smoothing operators on simulated data, whose T-F properties are known through construction. Finally, we analyze empirical data from eyes-closed surface electroencephalography recorded in human subjects to investigate alpha-band synchronization. These analyses show that selectively smoothing the auto spectra reduces the bias of the estimator and may improve the detection of T-F interdependence in electrophysiological data at high temporal resolution

Characterizing dynamically evolving functional networks in humans with application to speech

Understanding how communication between brain areas evolves to support dynamic function remains a fundamental challenge in neuroscience. One approach to this question is functional connectivity analysis, in which statistical coupling measures are employed to detect signatures of interactions between brain regions. Because the brain uses multiple communication mechanisms at different temporal and spatial scales, and because the neuronal signatures of communication are often weak, powerful connectivity inference methodologies require continued development specific to these challenges. Here we address the challenge of inferring task-related functional connectivity in brain voltage recordings. We first develop a framework for detecting changes in statistical coupling that occur reliably in a task relative to a baseline period. The framework characterizes the dynamics of connectivity changes, allows inference on multiple spatial scales, and assesses statistical uncertainty. This general framework is modular and applicable to a wide range of tasks and research questions. We demonstrate the flexibility of the framework in the second part of this thesis, in which we refine the coupling statistics and hypothesis tests to improve statistical power and test different proposed connectivity mechanisms. In particular, we introduce frequency domain coupling measures and define test statistics that exploit theoretical properties and capture known sampling variability. The resulting test statistics use correlation, coherence, canonical correlation, and canonical coherence to infer task-related changes in coupling. Because canonical correlation and canonical coherence are not commonly used in functional connectivity analyses, we derive the theoretical values and statistical estimators for these measures. In the third part of this thesis, we present a sample application of these techniques to electrocorticography data collected during an overt reading task. We discuss the challenges that arise with task-related human data, which is often noisy and underpowered, and present functional connectivity results in the context of traditional and contemporary within-electrode analytics. In two of nine subjects we observe time-domain and frequency-domain network changes that accord with theoretical models of information routing during motor processing. Taken together, this work contributes a methodological framework for inferring task-related functional connectivity across spatial and temporal scales, and supports insight into the rapid, dynamic functional coupling of human speech