Multitaper Spectral Estimation Research Articles

Event couple spectral ratio <i>Q</i> method for earthquake clusters: application to northwest Bohemia

Abstract. We develop an amplitude spectral ratio method for event couples from clustered earthquakes to estimate seismic wave attenuation (Q−1) in the source volume. The method allows to study attenuation within the source region of earthquake swarms or aftershocks at depth, independent of wave path and attenuation between source region and surface station. We exploit the high-frequency slope of phase spectra using multitaper spectral estimates. The method is tested using simulated full wave-field seismograms affected by recorded noise and finite source rupture. The synthetic tests verify the approach and show that solutions are independent of focal mechanisms but also show that seismic noise may broaden the scatter of results. We apply the event couple spectral ratio method to northwest Bohemia, Czech Republic, a region characterized by the persistent occurrence of earthquake swarms in a confined source region at mid-crustal depth. Our method indicates a strong anomaly of high attenuation in the source region of the swarm with an averaged attenuation factor of Qp<100. The application to S phases fails due to scattered P-phase energy interfering with S phases. The Qp anomaly supports the common hypothesis of highly fractured and fluid saturated rocks in the source region of the swarms in northwest Bohemia. However, high temperatures in a small volume around the swarms cannot be excluded to explain our observations.

Position-Specific Statistics of 60 GHz Vehicular Channels During Overtaking

The time-variant vehicle-to-vehicle radio propagation channel in the frequency band from 59.75 to 60.25 GHz has been measured in an urban street in the city center of Vienna, Austria. We have measured a set of 30 vehicle-to-vehicle channel realizations to capture the effect of an overtaking vehicle. Our experiment was designed for characterizing the large-scale fading and the small-scale fading depending on the overtaking vehicle’s position. We demonstrate that large overtaking vehicles boost the mean receive power by up to 10 dB. The analysis of the small-scale fading reveals that the two-wave with diffuse power (TWDP) fading model is adequate. By means of the model selection, we demonstrate the regions where the TWDP model is more favorable than the customarily used the Rician fading model. Furthermore, we analyze the time selectivity of our vehicular channel. To precisely define the Doppler and delay resolutions, a multitaper spectral estimator with discrete prolate spheroidal windows is used. The delay and Doppler profiles are inferred from the estimated local scattering function. Spatial filtering by the transmitting horn antenna decreases the delay and Doppler spread values. We observe that the RMS Doppler spread is below one-tenth of the maximum Doppler shift 2f v/c. For example, at 60 GHz, a relative speed of 30 km/h yields a maximum Doppler shift of approximately 3300 Hz. The maximum RMS Doppler spread of all observed vehicles is 450 Hz; the largest observed RMS delay spread is 4 ns.

Electroencephalogram dynamics during general anesthesia predict the later incidence and duration of burst-suppression during cardiopulmonary bypass

ObjectiveElectroencephalogram burst-suppression during general anesthesia is associated with post-operative delirium (POD). Whether burst-suppression causes POD or merely reflects susceptibility to POD is unclear. We hypothesized decreased intraoperative alpha (8–12 Hz) and beta (13–33 Hz) power prior to the occurrence of burst-suppression in susceptible patients. MethodsWe analyzed intraoperative electroencephalogram data of cardiac surgical patients undergoing cardiopulmonary bypass (CPB). We detected the incidence and duration of CPB burst-suppression with an automated burst-suppression detection algorithm. We analyzed EEG data with multitaper spectral estimation methods. We assessed associations between patient characteristics and burst-suppression using Binomial and Zero-inflated Poisson Regression Models. ResultsWe found significantly decreased alpha and beta power (7.8–22.95 Hz) in the CPB burst-suppression cohort. The odds ratio for the association between point estimates for alpha and beta power (7.8–22.95 Hz) and the incidence of burst-suppression was 0.88 (95% CI: 0.79–0.98). The incidence rate ratio for the association between point estimates for power between the alpha and beta range and the duration of burst-suppression was 0.89 (95% CI: 0.84–0.93). ConclusionDecreased intra-operative power within the alpha and beta range was associated with susceptibility to burst-suppression during CPB. SignificanceThis dynamic may be used to develop principled neurophysiological-based approaches to aid the preemptive identification and targeted care of POD vulnerable patients.

Optimally band-limited spectroscopy of control noise using a qubit sensor

Classical control noise is ubiquitous in qubit devices, making its accurate spectral characterization essential for designing optimized error suppression strategies at the physical level. Here, we focus on multiplicative Gaussian amplitude control noise on a driven qubit sensor and show that sensing protocols using optimally band-limited Slepian modulation offer substantial benefit in realistic scenarios. Special emphasis is given to laying out the theoretical framework necessary for extending non-parametric multitaper spectral estimation to the quantum setting by highlighting key points of contact and differences with respect to the classical formulation. In particular, we introduce and analyze two approaches (adaptive vs. single-setting) to quantum multitaper estimation, and show how they provide a practical means to both identify fine spectral features not otherwise detectable by existing protocols and to obtain reliable prior estimates for use in subsequent parametric estimation, including high-resolution Bayesian techniques. We quantitatively characterize the performance of both single- and multitaper Slepian estimation protocols by numerically reconstructing representative spectral densities, and demonstrate their advantage over dynamical-decoupling noise spectroscopy approaches in reducing bias from spectral leakage as well as in compensating for aliasing effects while maintaining a desired sampling resolution.

MSE Estimates for Multitaper Spectral Estimation and Off-Grid Compressive Sensing

We obtain estimates for the mean squared error (MSE) for the multitaper spectral estimator and certain compressive acquisition methods for multi-band signals. We confirm a fact discovered by Thomson [Spectrum estimation and harmonic analysis, Proc. IEEE, 1982]: assuming bandwidth $W$ and $N$ time domain observations, the average of the square of the first $K=\lfloor 2NW\rfloor$ Slepian functions approaches, as $K$ grows, an ideal bandpass kernel for the interval $[ -W,W]$ . We provide an analytic proof of this fact and measure the corresponding rate of convergence in $L^{1}$ norm. This validates a heuristic approximation used to control the MSE of the multitaper estimator. The estimates have also consequences for the method of compressive acquisition of multi-band signals introduced by Davenport and Wakin, giving MSE approximation bounds for the dictionary formed by modulation of the critical number of prolates.

Multitaper perceptual linear prediction features of voice samples to discriminate healthy persons from early stage Parkinson diseased persons

The performance of multitaper perceptual linear prediction (PLP) features of speech samples to discriminate healthy and early stage Parkinson diseased subjects is investigated in this paper. The PLP features are conventionally obtained by computing the power spectrum using a single tapered Hamming window. This estimated spectrum exhibits large variance which can be reduced by computing the weighted average of power spectra obtained using a set of tapered windows, leading to multitaper spectral estimation. In this investigation, two multitaper techniques namely Sine wave taper and Thomson multitaper along with the conventional single taper windowing are investigated. Artificial Neural network is then used to classify the PLP features extracted by applying the three types of window tapers on the speech signals of healthy and early stage Parkinson affected people and their respective performances are compared. The results show more accuracy using the multitaper techniques when compared with the conventional single taper technique. It is seen that the accuracy obtained using Sine wave tapers as well as Thomson multitaper is maximum for five tapers. An improvement in the recognition accuracy by 7.5% using the Sine tapers and by 6.9% using the Thomson tapers is obtained when compared with the conventional method. An improvement in other performance measures like Equal error rate, False positive rate, False negative rate, Sensitivity and Specificity is also observed in the multitaper techniques.

A frequency recognition method based on multitaper spectral analysis and SNR estimation for SSVEP-based brain-computer interface.

Over the past several years, steady-state visual evoked potential (SSVEP)-based brain-computer interfaces (BCIs) have attracted wide attention in the field of BCIs research due to high information transfer rate, little user training, and applicability to the majority. In conventional recognition methods for training-free SSVEP-based BCIs, the energy difference between the frequencies of electroencephalogram (EEG) background noise is usually ignored, therefore, there is a significant variance among the recognition accuracy of different stimulus frequencies. In order to improve the performance of training-free SSVEP-based BCIs system and balance the accuracy of recognition between different stimulus frequencies, a recognition method based on multitaper spectral analysis and signal-to-noise ratio estimation (MTSA-SNR) is proposed in this paper. A 40-class SSVEP public benchmark SSVEP dataset recorded from 35 subjects was used to evaluate the performance of the proposed method. Under the condition of 2.25s data length, the accuracy of the three methods were 81.1% (MTSA-SNR), 74.5% (canonical correlation analysis, CCA) and 73.4% (multivariate synchronization index, MSI), and the corresponding ITRs were 101 bits/min (MTSA-SNR), 89 bits/min (CCA), 87 bits/min (MSI). In the low frequency range (8-9.8Hz), the average recognition accuracy of the three methods is 82.9% (MTSA-SNR), 82.0% (CCA), 83.3% (MSI). The average accuracy of the three methods was 78.6% (MTSA-SNR), 64.9% (CCA) and 61.8% (MSI) in the high frequency range (14-15.8Hz). According to the results, the proposed method can effectively improve the performance of training-free SSVEP-based BCI system, and balance the recognition accuracy between different stimulation frequencies.

Evaluation of a novel median power spectrogram for seizure detection by non-neurophysiologists

Purpose(1) To evaluate how well resident physicians use a novel EEG spectral analysis tool (the median power spectrogram; MPS) to detect seizures. (2) To assess the capability of the MPS to identify different seizure types. Methods120 EEG records from children with intractable seizures were converted to MPS by taking the median power across leads and using multi-taper spectral estimation. Twelve blinded neurology residents were trained to interpret the spectrogram with a five-minute video tutorial and post-test. Two residents independently assessed each set for presence of seizures. Their performance was compared to seizures identified using conventional EEG. Two blinded neurologists separately reviewed the EEGs and spectrograms to independently categorize the seizures. Their results were used to determine the spectrogram’s capability to reveal seizures and visualize different seizure types for the user. ResultsThree key MPS features distinguished seizures from inter-ictal background: power difference relative to background, down-sloping resonance bands, and power in high frequencies. Using these features, residents identified seizures with 77% sensitivity and 72% specificity. 86% (51/59) of focal seizures and 81% (22/27) of generalized seizures were detected by at least one resident. Missed seizures included brief (<60s) seizures, tonic seizures, seizures with predominant delta (0–4Hz) activity, and seizures evident primarily in supplementary low temporal leads. ConclusionsThe MPS is a novel qEEG modality that requires minimal training to interpret. It enables physicians without extensive neurophysiology training to identify seizures with sensitivity and specificity comparable to more complex multi-modal qEEG displays.

Research on Speech Endpoint Detection Algorithm with Low SNR

The detection of speech endpoint is an important application for speech signal processing. Although there are variance methods, the endpoint can’t be detected accurately in low SNR (Signal to Noise Ratio). The paper pointes out an endpoint detection algorithm combining two methods together: the one is improved spectral subtraction based on multitaper spectral estimation, and the other is BARK subband variance in frequency domain. Firstly, the noisy speech signal is processed though the improved spectral subtraction based on multitaper spectral estimation. It can achieve the purpose of noise reduction through this step. Then the noisy speech signal is detected using the method of BARK subband variance in frequency domain. Compared with the common endpoint detection algorithm, it is concluded that endpoint detection accuracy by new method can be improved in low SNR.

Spectrum Sensing Optimization and Performance Enhancement of Cognitive Radio Networks

Cognitive radio (CR) is an attractive approach to face the shortage in the electromagnetic spectrum resources and improve the overall spectrum utilization. In this paper, two spectrum sensing techniques are considered for CR networks; one based on energy detection and the other based on multi-taper spectral estimation. Energy detector (ED) is examined in detail for both single user and cooperative multiple users using K out of M fusion rule. Simulation results in both scenarios are evaluated and verified using a Genetic Algorithm optimizer. The results show that cooperative sensing is better in performance than standalone sensing. The superiority of the Multi-taper spectral estimator (MSE) to the ED is comprehensively explained for a single secondary user scenario. The probability of detection at different target false alarm probabilities is evaluated. Simulation results show that MSE outperforms the ED by about 10 dB. Simulation results also show that as the target false alarm probability is decreased, the required Signal-to-Noise Ratio to achieve the same probability of detection gets higher.

East Asian monsoon signals reflected in temperature and precipitation changes over the past 300 years in the middle and lower reaches of the Yangtze River.

Based on observational data and Asian monsoon intensity datasets from China, the relationships between the East Asian winter monsoon index and winter temperature, the East Asian summer monsoon index and Meiyu precipitation over the middle and lower reaches of the Yangtze River, were analyzed. We found that the monsoon signals were reflected in the temperature and Meiyu precipitation variations. Thus, we used the reconstructed Meiyu precipitation and winter temperature series for the past 300 years and detected the summer/winter monsoon intensity signals using multi-taper spectral estimation method and wavelet analysis. The main periodicities of Meiyu precipitation and winter temperature, such as interannual cycle with 2–7-year, interdecadal-centennial cycles with 30–40-year and 50–100-year, were found. The good relationships between the East Asian summer and winter monsoons suggested that they were in phase at 31-year cycle, while out of phase at 100-year cycle, but with 20-year phase difference. In addition, the winter monsoon intensity may be regulated by the North Atlantic Oscillation, the Arctic Oscillation and the Atlantic Multidecadal Oscillation, and the summer monsoon is closely related to the signal intensities of the Pacific Decadal Oscillation.

A review of multitaper spectral analysis.

Nonparametric spectral estimation is a widely used technique in many applications ranging from radar and seismic data analysis to electroencephalography (EEG) and speech processing. Among the techniques that are used to estimate the spectral representation of a system based on finite observations, multitaper spectral estimation has many important optimality properties, but is not as widely used as it possibly could be. We give a brief overview of the standard nonparametric spectral estimation theory and the multitaper spectral estimation, and give two examples from EEG analyses of anesthesia and sleep.

Observed periodicities and the spectrum of field variations in Holocene magnetic records

In order to understand mechanisms that maintain and drive the evolution of the Earthʼs magnetic field, a characterization of its behavior on time scales of centuries to millennia is required. We have conducted a search for periodicities in Holocene sediment magnetic records, by applying three techniques: multitaper spectral estimation, wavelet analysis and empirical mode decomposition. When records are grouped according to their geographical locations, we find encouraging consistency amongst the observed periods, especially in nearby inclination records. No evidence was obtained for discrete, globally observed, periods. Rather we find a continuous broadband spectrum, with a slope corresponding to a power law with exponent of −2.3±0.6 for the period range between 300 and 4000 yr. This is consistent with the hypothesis that chaotic convection in the outer core drives the majority of secular variation.

Dynamic changes in direction and frequency range of inter-areal cortical interactions revealed by non-parametric Granger causality

Models suggest that communication between brain areas could be mediated by oscillations in specific frequency bands. This hypothesis is supported by electrophysiological measurements wherein direction and frequency of interaction between brain areas varied during different stages of a cognitive task. Frequency-resolved granger causality (GC) is used often for this analysis, but it has been derived for stationary linear processes, which may not be appropriate for brain activity. Our goal was to determine whether for nonlinear processes conditional GC could still distinguish direct connections from indirect ones and to what extent dynamic changes in frequency & direction of interaction could be accurately detected. For this properties of GC determined parametrically, through fitting an autoregressive process of a fixed order, were compared to those obtained via non-parametric GC, which only uses measured spectral matrix. Oscillations in each cortical area were represented by a low-dimensional nonlinear model driven by white noise, whose standard deviation represented level of activity in respective areas. In addition, we analyzed responses from two coupled networks of spiking neurons in same way. We found that direction of interaction between reciprocally connected cortical areas was determined by level of activity, going from areas with high activity to those with low activity, which could be modulated on fast time scales. The frequency band of interaction was determined by sending area. For linear processes, parametric GC had lowest bias and variance compared to non-parametric GC, but was not appropriate for nonlinear model and network model, because oscillations could not be modeled accurately by autoregressive processes of a reasonable order. The non-parametric GC correctly represented ground truth connectivity when multi-taper spectral estimates were used, but when multi-tapering made spectral peaks too broad, artifacts emerged. Taken together, GC analysis revealed a simple rule for direction and frequency band of communication between cortical areas, specifically the loudest area gets heard, which can account for recent experimental results in which frequency band of communication was direction dependent.

Multitaper spectral method to estimate the elastic thickness of South China: Implications for intracontinental deformation

The effective elastic thickness (Te) represents the thickness of the elastic layer or the flexural rigidity of the lithosphere, the equivalent of which can be calculated from the spectral analysis of gravity and topographic data. Studies of Te have profound influence on intracontinental deformation, and coupling of the tectonic blocks. In this paper, we use the multitaper spectral estimation method to calculate the coherence between Bouguer gravity and topography data, and to obtain the Te map of South China. Through the process of correction, we discuss the relationships of Te versus heat flow, and Te versus seismicity. The results show that Te distribution of South China is affected by three factors: the original age, which controls the basic feature; the Mesozoic evolution, which affects the Te distribution; and the neotectonic movement, which shaped the final distribution. The crust age has a positive correlation with the first-order Te distribution; thus the Yangtze Craton has a relatively higher Te (about 50 km) whereas the Te in Cathaysia block is only 10–20 km. By analysis and comparison among the tectonic models of South China, the Te distribution can be well explained using the flat-subduction model. As is typical with neotectonics, the region with a higher heat flow is related with a lower Te. The seismicity does not have a clear relationship with Te, but the strong seismicity could cause a low Te. Seismogenic layer (Ts) has a similar trend as Te in the craton, whereas in other areas the relationship is complex.

Multitaper MFCC and PLP features for speaker verification using i-vectors

In this paper we study the performance of the low-variance multi-taper Mel-frequency cepstral coefficient (MFCC) and perceptual linear prediction (PLP) features in a state-of-the-art i-vector speaker verification system. The MFCC and PLP features are usually computed from a Hamming-windowed periodogram spectrum estimate. Such a single-tapered spectrum estimate has large variance, which can be reduced by averaging spectral estimates obtained using a set of different tapers, leading to a so-called multi-taper spectral estimate. The multi-taper spectrum estimation method has proven to be powerful especially when the spectrum of interest has a large dynamic range or varies rapidly. Multi-taper MFCC features were also recently studied in speaker verification with promising preliminary results. In this study our primary goal is to validate those findings using an up-to-date i-vector classifier on the latest NIST 2010 SRE data. In addition, we also propose to compute robust perceptual linear prediction (PLP) features using multitapers. Furthermore, we provide a detailed comparison between different taper weight selections in the Thomson multi-taper method in the context of speaker verification. Speaker verification results on the telephone (det5) and microphone speech (det1, det2, det3 and det4) of the latest NIST 2010 SRE corpus indicate that the multi-taper methods outperform the conventional periodogram technique. Instead of simply averaging (using uniform weights) the individual spectral estimates in forming the multi-taper estimate, weighted averaging (using non-uniform weights) improves performance. Compared to the MFCC and PLP baseline systems, the sine-weighted cepstrum estimator (SWCE) based multitaper method provides average relative reductions of 12.3% and 7.5% in equal error rate, respectively. For the multi-peak multi-taper method, the corresponding reductions are 12.6% and 11.6%, respectively. Finally, the Thomson multi-taper method provides error reductions of 9.5% and 5.0% in EER for MFCC and PLP features, respectively. We conclude that both the MFCC and PLP features computed via multitapers provide systematic improvements in recognition accuracy.

Spectral estimation for geophysical time-series with inconvenient gaps

SUMMARY The power of spectral estimation as a tool for studying geophysical processes is often limited by short records or breaks in available time-series. Direct spectral estimation using multitaper techniques designed to reduce variance and minimize leakage can help alleviate the first problem. For records with gaps, systematic interpolation or averaging of multitaper spectra derived from record fragments may prove adequate in some cases, but can be cumbersome to implement. Alternatively, multitapers can be modified for use in direct spectral estimation with intermittently sampled data. However, their performance has not been adequately studied. We investigate reliability and resolution of techniques that adapt prolate and minimum bias (MB) multitapers to accommodate the longest breaks in sampling, comparing the tapering functions (referred to as PRG or MBG tapers) with the standard prolate and MB tapers used for complete data series, and with the section-averaging approach. Using a synthetic data set, we test both jackknife and bootstrap methods to calculate confidence intervals for PRG and MBG multitaper spectral estimates and find the jackknife is both more accurate and faster to compute. To implement these techniques for a variety of data sets, we provide an algorithm that allows the user to balance judicious interpolation against the use of suitably adapted tapers, providing empirical measures of both bias and frequency resolution for candidate sets of tapers. These techniques are tested on diverse geophysical data sets: a record of change in the length of day, a model of the external dipole part of the geomagnetic field produced by the magnetospheric ring current, and a 12 Myr long irregularly sampled relative geomagnetic palaeointensity record with pernicious gaps. We conclude that both PRG and MBG tapers generally perform as well as, or better than, an optimized form of the commonly used section averaging approach. The greatest improvements seem to occur when the gap structure creates data segments of very unequal lengths. Ease of computation and more robust behaviour can make MBG tapers a better choice than PRG except when very fine-scale frequency resolution is required. These techniques could readily be applied for cross-spectral and transfer function estimation and are a useful addition to the geophysical toolbox.

Changing spectrum of geomagnetic intensity variations in a fragmented 12 My sediment record from the Oligocene

Time series of relative geomagnetic paleointensity variations derived from marine sediments can be calibrated using absolute data derived from igneous materials. The resulting records may be suitable for spectral analysis of geomagnetic dipole variations. This work re-evaluates the 12 My (22.74–34.77 Ma) sediment record from Deep Sea Drilling Project Leg 73, Site 522, that is a key data set for determining the paleomagnetic power spectrum in the frequency range 1–100 My −1. The 12 My record is marred by uneven sampling, with the interval between samples ranging from 1 to 640 ky, and contains several gaps that are considered too long to interpolate. The relative intensity data are calibrated using 129 globally distributed absolute paleointensity data from the same time interval. The power spectrum of the resulting time series is estimated using direct multi-taper spectral estimation with prolate data tapers adapted to deal with missing sections in the time series. The longest record available for analysis is thereby extended from 5.3 to 12 My. The new paleomagnetic power spectrum confirms the presence of a broad spectral peak at around 8 My −1 for the early Oligocene and uncovers a peak around 2.5 My −1 in the late Oligocene. Both peaks may be linked to tiny wiggles in marine magnetic anomalies. The new analysis unambiguously verifies that there is lower overall power in the younger part of the record, where the reversal process appears to dominate the power spectrum of the paleosecular variation. A comparison of the late Oligocene spectrum with that of PADM2M, a model of paleomagnetic axial dipole variations for 0–2 Ma, reveals some broad similarities; both time periods have similar power levels and a reversal rate of 4 My −1. During the early Oligocene the reversal rate is about a factor of two lower, the field strength is higher, and the secular variation is stronger, suggesting that a strong magnetic field inhibits reversals but produces more variability in field strength.

The Effect of Spectral Estimation on Speech Enhancement Performance

It has long been observed that accuracy in spectral estimation greatly affects the quality of enhanced speech. A small decrease in the bias and variance of the estimator can greatly reduce the amount of residual noise and distortion in the recovered speech. To date, however, there has been little interest in a rigorous analysis quantifying such observations. In this paper, we analyze the effect of spectral estimate variance on enhanced speech as measured by quantitative and qualitative means. The performance analysis is derived for the signal subspace and the minimum mean square error short-time spectral amplitude estimators. Error is defined as the random function of frequency given by the difference between the estimated and the true power spectral density (PSD) functions. It is measured by its variance as a fraction of the clean speech PSD squared: a norm called the variance quality factor (VQF). The error VQF is derived in terms of the VQF of measurable quantities such as noisy speech and noise alone. It is shown that reducing the PSD estimate variance reduces significantly the VQF of the enhancement error. We provide analytical derivations to establish the results and accompanying simulations to confirm the theoretical analysis. Simulations test the periodogram, Blackman-Tukey, Bartlett-Welch, and Multitaper spectral estimation methods.

Understanding changes over time in workers' compensation claim rates using time series analytical techniques

ObjectiveThe objective of this study is to better understand the inter-temporal variation in workers' compensation claim rates using time series analytical techniques not commonly used in the occupational health and...