On the Selection of Optimum Savitzky-Golay Filters

Savitzky-Golay (S-G) filters are finite impulse response lowpass filters obtained while smoothing data using a local least-squares (LS) polynomial approximation. Savitzky and Golay proved in their hallmark paper that local LS fitting of polynomials and their evaluation at the mid-point of the approximation interval is equivalent to filtering with a fixed impulse response. The problem that we address here is, ``how to choose a pointwise minimum mean squared error (MMSE) S-G filter length or order for smoothing, while preserving the temporal structure of a time-varying signal.'' We solve the bias-variance tradeoff involved in the MMSE optimization using Stein's unbiased risk estimator (SURE). We observe that the 3-dB cutoff frequency of the SURE-optimal S-G filter is higher where the signal varies fast locally, and vice versa, essentially enabling us to suitably trade off the bias and variance, thereby resulting in near-MMSE performance. At low signal-to-noise ratios (SNRs), it is seen that the adaptive filter length algorithm performance improves by incorporating a regularization term in the SURE objective function. We consider the algorithm performance on real-world electrocardiogram (ECG) signals. The results exhibit considerable SNR improvement. Noise performance analysis shows that the proposed algorithms are comparable, and in some cases, better than some standard denoising techniques available in the literature.

Time-Optimal Convergence to a Rectilinear Path in the Presence of Wind

This paper considers the problem of determining the time-optimal path of a fixed-wing Miniature Air Vehicle (MAV), in the presence of wind. The MAV, which is subject to a bounded turn rate, is required to eventually converge to a straight line starting from a known initial position and orientation. Earlier work in the literature uses Pontryagin's Minimum Principle (PMP) to solve this problem only for the no-wind case. In contrast, the present work uses a geometric approach to solve the problem completely in the presence of wind. In addition, it also shows how PMP can be used to partially solve the problem. Using a 6-DOF model of a MAV the generated optimal path is tracked by an autopilot consisting of proportional-integral-derivative (PID) controllers. The simulation results show the path generation and tracking for cases with steady and time-varying wind. Some issues on real-time path planning are also addressed.

Identification of nonlinear dynamic systems: Time-frequency filtering and skeleton curves

The nonlinear behavior varying with the instantaneous response was analyzed through the joint time-frequency analysis method for a class of S. D. O. F nonlinear system. A masking operator an definite regions is defined and two theorems are presented. Based on these, the nonlinear system is modeled with a special time-varying linear one, called the generalized skeleton linear system (GSLS). The frequency skeleton curve and the damping skeleton curve are defined to describe the main feature of the non-linearity as well. Moreover, an identification method is proposed through the skeleton curves and the time-frequency filtering technique.

Time Variation in an Optimal Asymmetric Preference Monetary Policy Model

This paper considers a time varying parameter extension of the Ruge-Murcia (2003, 2004) model to explore whether some of the variation in parameter estimates seen in the literature could arise from this source. A time varying value for the unemployment volatility parameter can be motivated through several means including variation in the slope of the Phillips curve or variation in the preferences of the monetary authority.We show that allowing time variation for the coefficient on the unemployment volatility parameter improves the model fit and it helps to provide an explanation of inflation bias based on asymmetric central banker preferences, which is consistent across subsamples.

Time-frequency spectral estimation of speech

In recent years there has been a growing interest amongst the speech research community into the use of spectral estimators which circumvent the traditional quasi-stationary assumption and provide greater time-frequency (t-f) resolution than conventional spectral estimators, such as the short time Fourier power spectrum (STFPS). One distribution in particular, the Wigner distribution (WD), has attracted considerable interest. However, experimental studies have indicated that, despite its improved t-f resolution, employing the WD as the front end of speech recognition system actually reduces recognition performance; only by explicitly re-introducing t-f smoothing into the WD are recognition rates improved. In this paper we provide an explanation for these findings. By treating the spectral estimation problem as one of optimization of a bias variance trade off, we show why additional t-f smoothing improves recognition rates, despite reducing the t-f resolution of the spectral estimator. A practical adaptive smoothing algorithm is presented, whicy attempts to match the degree of smoothing introduced into the WD with the time varying quasi-stationary regions within the speech waveform. The recognition performance of the resulting adaptively smoothed estimator is found to be comparable to that of conventional filterbank estimators, yet the average temporal sampling rate of the resulting spectral vectors is reduced by around a factor of 10. © 1992.

Decentralised minimal-time dynamic consensus

This paper considers a group of agents that aim to reach an agreement on individually received time-varying signals by local communication. In contrast to static network averaging problem, the consensus considered in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises a minimal number of local observations of a randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically as suggested by Olshevsky and Tsitsiklis. © 2012 AACC American Automatic Control Council).

A dependent partition-valued process for multitask clustering and time evolving network modelling

The fundamental aim of clustering algorithms is to partition data points. We consider tasks where the discovered partition is allowed to vary with some covariate such as space or time. One approach would be to use fragmentation-coagulation processes, but these, being Markov processes, are restricted to linear or tree structured covariate spaces. We define a partition-valued process on an arbitrary covariate space using Gaussian processes. We use the process to construct a multitask clustering model which partitions datapoints in a similar way across multiple data sources, and a time series model of network data which allows cluster assignments to vary over time. We describe sampling algorithms for inference and apply our method to defining cancer subtypes based on different types of cellular characteristics, finding regulatory modules from gene expression data from multiple human populations, and discovering time varying community structure in a social network.

A laboratory study on risk assessment of microcystin-RR in cropland

The persistence time and risk of microcystin-RR (MC-RR) in cropland via irrigation were investigated under laboratory conditions. In order to evaluate the efficiency of the potential adsorption and biodegradation of MC-RR in cropland and the persistence time of MC-RR for crop irrigation, high performance liquid chromatography (HPLC) was used to quantify the amount of MC-RR in solutions. Our study indicated that MC-RR could be adsorbed and biodegraded in cropland soils. MC-RR at 6.5 mg/L could be completely degraded within 6 days with a lag phase of 1 - 2 days. In the presence of humic acid, the same amount of MC-RR could be degraded within 4 days without a lag phase. Accordingly, the persistence time of MC-RR in cropland soils should be about 6 days. This result also suggested the beneficial effects of the organic fertilizer utilization for the biodegradation of MC-RR in cropland soils. Our studies also demonstrated that MC-RR at low concentration (< 10 mu g/L) could accelerate the growth of plants, while high concentration of MC-RR (> 100 mu g/L) significantly inhibited the growth of plants. High sensitivity of the sprouting stage plants to MC-RR treatments as well as the strong inhibitory effects resulting from prolonged irrigation further indicated that this MC-RR growth-inhibition may vary with the duration of irrigation and life stage of the plants. (c) 2007 Published by Elsevier Ltd.

Time-Frequency Representations for Speech Signals

This work addresses two related questions. The first question is what joint time-frequency energy representations are most appropriate for auditory signals, in particular, for speech signals in sonorant regions. The quadratic transforms of the signal are examined, a large class that includes, for example, the spectrograms and the Wigner distribution. Quasi-stationarity is not assumed, since this would neglect dynamic regions. A set of desired properties is proposed for the representation: (1) shift-invariance, (2) positivity, (3) superposition, (4) locality, and (5) smoothness. Several relations among these properties are proved: shift-invariance and positivity imply the transform is a superposition of spectrograms; positivity and superposition are equivalent conditions when the transform is real; positivity limits the simultaneous time and frequency resolution (locality) possible for the transform, defining an uncertainty relation for joint time-frequency energy representations; and locality and smoothness tradeoff by the 2-D generalization of the classical uncertainty relation. The transform that best meets these criteria is derived, which consists of two-dimensionally smoothed Wigner distributions with (possibly oriented) 2-D guassian kernels. These transforms are then related to time-frequency filtering, a method for estimating the time-varying 'transfer function' of the vocal tract, which is somewhat analogous to ceptstral filtering generalized to the time-varying case. Natural speech examples are provided. The second question addressed is how to obtain a rich, symbolic description of the phonetically relevant features in these time-frequency energy surfaces, the so-called schematic spectrogram. Time-frequency ridges, the 2-D analog of spectral peaks, are one feature that is proposed. If non-oriented kernels are used for the energy representation, then the ridge tops can be identified, with zero-crossings in the inner product of the gradient vector and the direction of greatest downward curvature. If oriented kernels are used, the method can be generalized to give better orientation selectivity (e.g., at intersecting ridges) at the cost of poorer time-frequency locality. Many speech examples are given showing the performance for some traditionally difficult cases: semi-vowels and glides, nasalized vowels, consonant-vowel transitions, female speech, and imperfect transmission channels.

Nonlinear Acoustics in Underwater and Biomedical Applications: Array Performance Degradation and Time Reversal Invariance

This dissertation describes a model for acoustic propagation in inhomogeneous flu- ids, and explores the focusing by arrays onto targets under various conditions. The work explores the use of arrays, in particular the time reversal array, for underwater and biomedical applications. Aspects of propagation and phasing which can lead to reduced focusing effectiveness are described. An acoustic wave equation was derived for the propagation of finite-amplitude waves in lossy time-varying inhomogeneous fluid media. The equation was solved numerically in both Cartesian and cylindrical geometries using the finite-difference time-domain (FDTD) method. It was found that time reversal arrays are sensitive to several debilitating factors. Focusing ability was determined to be adequate in the presence of temporal jitter in the time reversed signal only up to about one-sixth of a period. Thermoviscous absorption also had a debilitating effect on focal pressure for both linear and nonlinear propagation. It was also found that nonlinearity leads to degradation of focal pressure through amplification of the received signal at the array, and enhanced absorption in the shocked waveforms. This dissertation also examined the heating effects of focused ultrasound in a tissue-like medium. The application considered is therapeutic heating for hyperther- mia. The acoustic model and a thermal model for tissue were coupled to solve for transient and steady temperature profiles in tissue-like media. The Pennes bioheat equation was solved using the FDTD method to calculate the temperature fields in tissue-like media from focused acoustic sources. It was found that the temperature-dependence of the medium's background prop- erties can play an important role in the temperature predictions. Finite-amplitude effects contributed excess heat when source conditions were provided for nonlinear ef- fects to manifest themselves. The effect of medium heterogeneity was also found to be important in redistributing the acoustic and temperature fields, creating regions with hotter and colder temperatures than the mean by local scattering and lensing action. These temperature excursions from the mean were found to increase monotonically with increasing contrast in the medium's properties.

Neonatal EEG classification using atomic decomposition

The electroencephalogram (EEG) is an important noninvasive tool used in the neonatal intensive care unit (NICU) for the neurologic evaluation of the sick newborn infant. It provides an excellent assessment of at-risk newborns and formulates a prognosis for long-term neurologic outcome.The automated analysis of neonatal EEG data in the NICU can provide valuable information to the clinician facilitating medical intervention. The aim of this thesis is to develop a system for automatic classification of neonatal EEG which can be mainly divided into two parts: (1) classification of neonatal EEG seizure from nonseizure, and (2) classifying neonatal background EEG into several grades based on the severity of the injury using atomic decomposition. Atomic decomposition techniques use redundant time-frequency dictionaries for sparse signal representations or approximations. The first novel contribution of this thesis is the development of a novel time-frequency dictionary coherent with the neonatal EEG seizure states. This dictionary was able to track the time-varying nature of the EEG signal. It was shown that by using atomic decomposition and the proposed novel dictionary, the neonatal EEG transition from nonseizure to seizure states could be detected efficiently. The second novel contribution of this thesis is the development of a neonatal seizure detection algorithm using several time-frequency features from the proposed novel dictionary. It was shown that the time-frequency features obtained from the atoms in the novel dictionary improved the seizure detection accuracy when compared to that obtained from the raw EEG signal. With the assistance of a supervised multiclass SVM classifier and several timefrequency features, several methods to automatically grade EEG were explored. In summary, the novel techniques proposed in this thesis contribute to the application of advanced signal processing techniques for automatic assessment of neonatal EEG recordings.

Neuronal correlates of visual time perception at brief timescales.

Successful interaction with the world depends on accurate perception of the timing of external events. Neurons at early stages of the primate visual system represent time-varying stimuli with high precision. However, it is unknown whether this temporal fidelity is maintained in the prefrontal cortex, where changes in neuronal activity generally correlate with changes in perception. One reason to suspect that it is not maintained is that humans experience surprisingly large fluctuations in the perception of time. To investigate the neuronal correlates of time perception, we recorded from neurons in the prefrontal cortex and midbrain of monkeys performing a temporal-discrimination task. Visual time intervals were presented at a timescale relevant to natural behavior (<500 ms). At this brief timescale, neuronal adaptation--time-dependent changes in the size of successive responses--occurs. We found that visual activity fluctuated with timing judgments in the prefrontal cortex but not in comparable midbrain areas. Surprisingly, only response strength, not timing, predicted task performance. Intervals perceived as longer were associated with larger visual responses and shorter intervals with smaller responses, matching the dynamics of adaptation. These results suggest that the magnitude of prefrontal activity may be read out to provide temporal information that contributes to judging the passage of time.

A framework for state-based time-series analysis and prediction

Time-series analysis and prediction play an important role in state-based systems that involve dealing with varying situations in terms of states of the world evolving with time. Generally speaking, the world in the discourse persists in a given state until something occurs to it into another state. This paper introduces a framework for prediction and analysis based on time-series of states. It takes a time theory that addresses both points and intervals as primitive time elements as the temporal basis. A state of the world under consideration is defined as a set of time-varying propositions with Boolean truth-values that are dependent on time, including properties, facts, actions, events and processes, etc. A time-series of states is then formalized as a list of states that are temporally ordered one after another. The framework supports explicit expression of both absolute and relative temporal knowledge. A formal schema for expressing general time-series of states to be incomplete in various ways, while the concept of complete time-series of states is also formally defined. As applications of the formalism in time-series analysis and prediction, we present two illustrating examples.

Iterative Multiuser Detection and Decoding for DS-CDMA System With Space-Time Linear Dispersion

This paper considers a Q-ary orthogonal direct-sequence code-division multiple-access (DS-CDMA) system with high-rate space-time linear dispersion codes (LDCs) in time-varying Rayleigh fading multiple-input-multiple-output (MIMO) channels. We propose a joint multiuser detection, LDC decoding, Q-ary demodulation, and channel-decoding algorithm and apply the turbo processing principle to improve system performance in an iterative fashion. The proposed iterative scheme demonstrates faster convergence and superior performance compared with the V-BLAST-based DS-CDMA system and is shown to approach the single-user performance bound. We also show that the CDMA system is able to exploit the time diversity offered by the LDCS in rapid-fading channels.

The finding of reduced estimated glomerular filtration rate is associated with increased mortality in a large UK population

BACKGROUND: CKD as defined by KDIGO/KDOQI has been shown to affect ~ 8.5% of the UK population. The prevalence of CKD in the UK is similar to that in the USA, yet incident dialysis rates are dramatically different. This retrospective cohort study investigates the association between reduced kidney function and mortality in a large UK population. METHODS: All serum creatinine results covering Northern Ireland's 1.7 million population were collected between 1 January 2001 and 31 December 2002. Estimated glomerular filtration rates (eGFR) were calculated for all serum creatinine measurements using four-variable MDRD equation (IDMS aligned). Patients were followed up for both all-cause and cardiovascular mortality data until the end of December 2006. Patients on renal replacement therapy were excluded. Subgroup analysis in the 75 345 subjects enrolled within a parallel primary care study permitted additional survival analysis with adjustment for traditional cardiovascular risk factors. RESULTS: A total of 1 967 827 serum creatinine results from 533 798 patients were collected. During the period of follow-up, 59 980 deaths occurred. In multivariate survival analysis, using eGFR as a time-varying covariate, a graded association between CKD (defined by eGFR) and all-cause mortality was identified. Compared with participants with an eGFR of > 60 mL/min/1.73 m(2), the adjusted hazard ratios (and 95% confidence intervals) for participants with an eGFR of 45-59 mL/min/1.73 m(2) was 1.02 (0.99-1.04), an eGFR of 30-44 mL/min/1.73 m(2) was 1.44 (1.40-1.47), an eGFR of 15-29 mL/min/1.73 m(2) was 2.12 (2.05-2.20) and an eGFR of