Optimal Window Length Research Articles

Determining the Optimal Window Length for Pattern Recognition-Based Myoelectric Control: Balancing the Competing Effects of Classification Error and Controller Delay

Pattern recognition-based control of myoelectric prostheses has shown great promise in research environments, but has not been optimized for use in a clinical setting. To explore the relationship between classification error, controller delay, and real-time controllability, 13 able-bodied subjects were trained to operate a virtual upper-limb prosthesis using pattern recognition of electromyogram (EMG) signals. Classification error and controller delay were varied by training different classifiers with a variety of analysis window lengths ranging from 50 to 550 ms and either two or four EMG input channels. Offline analysis showed that classification error decreased with longer window lengths (p < 0.01 ). Real-time controllability was evaluated with the target achievement control (TAC) test, which prompted users to maneuver the virtual prosthesis into various target postures. The results indicated that user performance improved with lower classification error (p < 0.01 ) and was reduced with longer controller delay (p < 0.01 ), as determined by the window length. Therefore, both of these effects should be considered when choosing a window length; it may be beneficial to increase the window length if this results in a reduced classification error, despite the corresponding increase in controller delay. For the system employed in this study, the optimal window length was found to be between 150 and 250 ms, which is within acceptable controller delays for conventional multistate amplitude controllers.

Evaluation of EMG processing techniques using Information Theory

BackgroundElectromyographic signals can be used in biomedical engineering and/or rehabilitation field, as potential sources of control for prosthetics and orthotics. In such applications, digital processing techniques are necessary to follow efficient and effectively the changes in the physiological characteristics produced by a muscular contraction. In this paper, two methods based on information theory are proposed to evaluate the processing techniques.MethodsThese methods determine the amount of information that a processing technique is able to extract from EMG signals. The processing techniques evaluated with these methods were: absolute mean value (AMV), RMS values, variance values (VAR) and difference absolute mean value (DAMV). EMG signals from the middle deltoid during abduction and adduction movement of the arm in the scapular plane was registered, for static and dynamic contractions. The optimal window length (segmentation), abduction and adduction movements and inter-electrode distance were also analyzed.ResultsUsing the optimal segmentation (200 ms and 300 ms in static and dynamic contractions, respectively) the best processing techniques were: RMS, AMV and VAR in static contractions, and only the RMS in dynamic contractions. Using the RMS of EMG signal, variations in the amount of information between the abduction and adduction movements were observed.ConclusionsAlthough the evaluation methods proposed here were applied to standard processing techniques, these methods can also be considered as alternatives tools to evaluate new processing techniques in different areas of electrophysiology.

Estimation of the phase derivative using an adaptive window spectrogram

The paper introduces an adaptive-window-spectrogram-based method to directly estimate the phase derivative from a single fringe pattern. The proposed method relies on estimating the phase derivative using spectrogram peak detection for a set of different window lengths. Then the optimal window length is selected from the set by resolving the estimator's bias variance trade-off using the intersection of confidence intervals rule. Finally, the phase derivative estimate corresponding to the optimum window is selected. The method's applicability to phase derivative estimation is demonstrated using simulation and experimental results.

Adaptive window Wigner-Ville-distribution-based method to estimate phase derivative from optical fringes

We introduce an adaptive window Wigner-Ville-distribution-based method to directly estimate the phase derivative from a single fringe pattern. In the proposed method, the phase derivative is estimated by using the peak detection of the pseudo-Wigner-Ville distribution for a set of different window lengths. Then the optimal window length is selected from the set by resolving the estimator's bias variance trade-off, using the intersection of confidence intervals rule. Finally, the phase derivative estimate corresponding to the optimum window is selected. Simulation and experimental results are presented to demonstrate the method's applicability for the phase derivative estimation.

Fisher information in window censored renewal process data and its applications

Suppose we have a renewal process observed over a fixed length of time starting from a random time point and only the times of renewals that occur within the observation window are recorded. Assuming a parametric model for the renewal time distribution with parameter θ, we obtain the likelihood of the observed data and describe the exact and asymptotic behavior of the Fisher information (FI) on θ contained in this window censored renewal process. We illustrate our results with exponential, gamma, and Weibull models for the renewal distribution. We use the FI matrix to determine optimal window length for designing experiments with recurring events when the total time of observation is fixed. Our results are useful in estimating the standard errors of the maximum likelihood estimators and in determining the sample size and duration of clinical trials that involve recurring events associated with diseases such as lupus.

Investigation of Short-Term Changes in Visual Evoked Potentials With Windowed Adaptive Chirplet Transform

We propose a new application of the adaptive chirplet transform that involves partitioning signals into non-overlapping sequential segments. From these segments, the local time-frequency structures of the signal are estimated by using a four-parameter chirplet decomposition. Entitled the windowed adaptive chirplet transform (windowed ACT), this approach is applied to the analysis of visual evoked potentials (VEPs). It can provide a unified and compact representation of VEPs from the transient buildup to the steady-state portion with less computational cost than its non-windowed counterpart. This paper also details a method to select the optimal window length for signal segmentation. This approach will be useful for long-term signal monitoring as well as for signal feature extraction and data compression.

Estimating Local Ancestry in Admixed Populations

Large-scale genotyping of SNPs has shown a great promise in identifying markers that could be linked to diseases. One of the major obstacles involved in performing these studies is that the underlying population substructure could produce spurious associations. Population substructure can be caused by the presence of two distinct subpopulations or a single pool of admixed individuals. In this work, we focus on the latter, which is significantly harder to detect in practice. New advances in this research direction are expected to play a key role in identifying loci that are different among different populations and are still associated with a disease. We evaluated current methods for inference of population substructure in such cases and show that they might be quite inaccurate even in relatively simple scenarios. We therefore introduce a new method, LAMP (Local Ancestry in adMixed Populations), which infers the ancestry of each individual at every single-nucleotide polymorphism (SNP). LAMP computes the ancestry structure for overlapping windows of contiguous SNPs and combines the results with a majority vote. Our empirical results show that LAMP is significantly more accurate and more efficient than existing methods for inferring locus-specific ancestries, enabling it to handle large-scale datasets. We further show that LAMP can be used to estimate the individual admixture of each individual. Our experimental evaluation indicates that this extension yields a considerably more accurate estimate of individual admixture than state-of-the-art methods such as STRUCTURE or EIGENSTRAT, which are frequently used for the correction of population stratification in association studies.

ZigBee-based wireless sensor networks for monitoring animal presence and pasture time in a strip of new grass

The problem of online monitoring of cows’ presence and pasture time in an extended area covered by a strip of new grass using wireless sensor networks has been addressed. The total pasture time in the extended area was estimated by measuring the pasture time in a specific part of that area called the gateway connectivity area where sensor nodes mounted on the cows could communicate directly with a gateway. Packet loss causes a node that was present in the connectivity range of the gateway frequently to be classified as an absent node. Therefore, a moving average window with optimal window length and threshold was designed to minimize the misclassification. As the measured pasture time in the gateway connectivity area was an underestimation of the total pasture time in the extended area, an area-based correction factor, same for all individual animals was applied. As only 23% of the animals in a herd were equipped to be monitored by sensor nodes, investigations to evaluate if the monitored number of animals could represent the whole herd were of great importance. To accomplish the investigations, the number of monitored cows by sensor nodes and the total number of cows (with and without sensor nodes) in the extended area were counted manually each minute over a period of 3 h during 3 days. Pearson chi-square test of goodness of fit showed that the number of cows in the extended area was normally distributed. Furthermore, a statistical test showed that the mean number of monitored cows in the extended area and the mean of total number of cows in the extended area corresponded with the percentage of monitored cows by sensor nodes in the herd (23%).

On Multiplicative Transfer Function Approximation in the Short-Time Fourier Transform Domain

The multiplicative transfer function (MTF) approximation is widely used for modeling a linear time invariant system in the short-time Fourier transform (STFT) domain. It relies on the assumption of a long analysis window compared with the length of the system impulse response. In this paper, we investigate the influence of the analysis window length on the performance of a system identifier that utilizes the MTF approximation. We derive analytic expressions for the minimum mean-square error (MMSE) in the STFT domain and show that the system identification performance does not necessarily improve by increasing the length of the analysis window. The optimal window length, that achieves the MMSE, depends on the signal-to-noise ratio and the length of the input signal. The theoretical analysis is supported by simulation results

An Adaptive Differentiation Filter for Tracking Instantaneous Frequency in Power Systems

This paper presents an application of adaptive differentiation filter in tracking instantaneous frequency in electrical power systems. For each new sample, the filter automatically selects an optimal window length that maximizes measurement accuracy. Large window length is selected if the frequency is slow varying or steady state, to increase efficiency in filtering noise and harmonics. For fast-varying frequency, the window length is automatically reduced in order to make frequency tracking more accurate, sacrificing filtering efficiency. Automatic selection of the optimal window length that balances between tracking and filtering performance is the unique feature of this technique. This paper concludes with the presentation of the representative results obtained in the simulation study as well as in some practical applications. The results show the adaptive differentiation filter gives accurate frequency measurement under both steady-state and dynamic conditions

Local linear approximation for tracking frequency in power systems

In this paper, we present an application of the local linear approximation technique in tracking power system frequency. Samples of the voltage phase angle are fitted using linear function. This approximation is valid locally on the left-sided window with variable length. The window slides with each new sample. The linear coefficient of the locally fitted function is the point estimate of the frequency deviation from the nominal value. For each new sample this technique automatically selects optimal window length in order to maximize estimation accuracy. A long window is selected if the frequency is slow varying, to increase efficiency in filtering noise and harmonics. For a fast varying frequency the window length automatically reduces in order to make frequency tracking more accurate but sacrificing on filtering efficiency. Automatic selection of the optimal window length that balances between tracking and filtering performance makes this technique very powerful in tracking frequency in a wider range, as required in generator control and protection applications. The paper concludes with the presentation of the representative simulation results.

A new method for adjusting neural response jitter in the STRF obtained by spike-trigger averaging

Sensitivity of central auditory neurons to frequency modulated (FM) sound is often characterized based on spectro-temporal receptive field (STRF), which is generated by spike-trigger averaging a random stimulus. Due to the inherent property of time variability in neural response, this method erroneously represents the response jitter as stimulus jitter in the STRF. To reveal the trigger features more clearly, we have implemented a method that minimizes this error. Neural spikes from the brainstem of urethane-anesthetized rats were first recorded in response to two sets of FM stimuli: (a) a random FM tone for the generation of STRF and (b) a family of linear FM ramps for the determination of FM ‘trigger point’. Based on the first dataset, STRFs were generated using spike-trigger averaging. Individual modulating waveforms were then matched with respect to their mean waveform at time-windows of a systematically varied length. A stable or optimal variance time profile was found at a particular window length. At this optimal window length, we performed delay adjustments. A marked sharpening in the FM bands in the STRF was found. Results were consistent with the FM ‘trigger point’ as estimated by the linear FM ramps. We concluded that the present approach of adjusting response jitter was effective in delineating FM trigger features in the STRF.

Improved Protein Secondary Structure Prediction Using Support Vector Machine With a New Encoding Scheme and an Advanced Tertiary Classifier

Prediction of protein secondary structures is an important problem in bioinformatics and has many applications. The recent trend of secondary structure prediction studies is mostly based on the neural network or the support vector machine (SVM). The SVM method is a comparatively new learning system which has mostly been used in pattern recognition problems. In this study, SVM is used as a machine learning tool for the prediction of secondary structure and several encoding schemes, including orthogonal matrix, hydrophobicity matrix, BLOSUM62 substitution matrix, and combined matrix of these, are applied and optimized to improve the prediction accuracy. Also, the optimal window length for six SVM binary classifiers is established by testing different window sizes and our new encoding scheme is tested based on this optimal window size via sevenfold cross validation tests. The results show 2% increase in the accuracy of the binary classifiers when compared with the instances in which the classical orthogonal matrix is used. Finally, to combine the results of the six SVM binary classifiers, a new tertiary classifier which combines the results of one-versus-one binary classifiers is introduced and the performance is compared with those of existing tertiary classifiers. According to the results, the Q3 prediction accuracy of new tertiary classifier reaches 78.8% and this is better than the best result reported in the literature.

Adaptive Window Zero-Crossing-Based Instantaneous Frequency Estimation

We address the problem of estimating instantaneous frequency (IF) of a real-valued constant amplitude time-varying sinusoid. Estimation of polynomial IF is formulated using the zero-crossings of the signal. We propose an algorithm to estimate nonpolynomial IF by local approximation using a low-order polynomial, over a short segment of the signal. This involves the choice of window length to minimize the mean square error (MSE). The optimal window length found by directly minimizing the MSE is a function of the higher-order derivatives of the IF which are not available a priori. However, an optimum solution is formulated using an adaptive window technique based on the concept of intersection of confidence intervals. The adaptive algorithm enables minimum MSE-IF (MMSE-IF) estimation without requiring a priori information about the IF. Simulation results show that the adaptive window zero-crossing-based IF estimation method is superior to fixed window methods and is also better than adaptive spectrogram and adaptive Wigner-Ville distribution (WVD)-based IF estimators for different signal-to-noise ratio (SNR).

Stable and Transportable Regional Magnitudes Based on Coda-Derived Moment-Rate Spectra

We describe an empirical calibration method for obtaining stable seismic source moment-rate spectra derived from regional coda envelopes using broadband stations. The results of applying this method yield source spectra that are more stable than any other direct-phase measure to date. The procedure accounts for all propagation, site, and S -to-coda transfer function effects. The resultant coda-derived moment-rate spectra are then used to provide traditional band-limited magnitudes (e.g., M L , m b ), as well as an unbiased, unsaturated magnitude (moment magnitude, M w ) that is tied to a physical measure of earthquake size (i.e., seismic moment). We validate our results by comparing our coda-derived moment estimates with those obtained from long-period waveform modeling. Most importantly, we demonstrate that the interstation magnitude scatter is significantly reduced when using long-window-length coda (i.e., M w (coda) and m b (coda)). However, when we use short-window coda measurements of 5 sec in length taken after twice the direct-wave travel time, the scatter remains large, comparable to direct waves. Once calibrated, the coda-derived source spectra provide stable, unbiased magnitude estimates for events that are too small either to be reliably waveform modeled or to be seen at far-regional and teleseismic distances. This property is ideal for sparse local or regional networks. We found that our source amplitude estimates were nearly insensitive to the expected source radiation pattern and exhibited roughly a factor of 3-5 less interstation scatter when compared against coda duration and conventional direct-phase measurements (e.g., P g , L g ). We also found that the coda stability, as measured by the interstation scatter for common events, reached a minimum value beyond a certain critical measurement window length. For example, at 6-8 Hz, the interstation standard deviation was less than 0.08 provided the coda measurement was at least ∼80 sec in duration, whereas at 1.5-2.0 Hz, the critical window length was ∼100 sec. For all frequency bands, as the coda window becomes shorter, the standard deviation increases, asymptotically approaching the direct-wave scatter. In this article we describe in detail the calibration methodology and address concerns related to choosing optimal measurement window lengths, estimating error, testing empirical path corrections, and tying coda amplitudes to an absolute scale. In order to demonstrate the usefulness and transportability of our method, we chose the Dead Sea Rift as our study area.

Adaptive instantaneous frequency estimation of multicomponent FM signals using quadratic time-frequency distributions

An adaptive approach to the estimation of the instantaneous frequency (IF) of nonstationary mono- and multicomponent FM signals with additive Gaussian noise is presented. The IF estimation is based on the fact that quadratic time-frequency distributions (TFDs) have maxima around the IF law of the signal. It is shown that the bias and variance of the IF estimate are functions of the lag window length. If there is a bias-variance tradeoff, then the optimal window length for this tradeoff depends on the unknown IF law. Hence, an adaptive algorithm with a time-varying and data-driven window length is needed. The adaptive algorithm can utilize any quadratic TFD that satisfies the following three conditions: First, the IF estimation variance given by the chosen distribution should be a continuously decreasing function of the window length, whereas the bias should be continuously increasing so that the algorithm will converge at the optimal window length for the bias-variance tradeoff, second, the time-lag kernel filter of the chosen distribution should not perform narrowband filtering in the lag direction in order to not interfere with the adaptive window in that direction; third, the distribution should perform effective cross-terms reduction while keeping high resolution in order to be efficient for multicomponent signals. A quadratic distribution with high resolution, effective cross-terms reduction and no lag filtering is proposed. The algorithm estimates multiple IF laws by using a tracking algorithm for the signal components and utilizing the property that the proposed distribution enables nonparametric component amplitude estimation. An extension of the proposed TFD consisting of the use of time-only kernels for adaptive IF estimation is also proposed.

The detection of cognitive state transitions by stability changes in event-related cortical field potentials

Cognitive tasks are characterized by sequences of stable states, which are thought to reflect distinct steps of neurocognitive processing. Here, we investigate a stability measure, derived from adaptive multivariate autoregressive (AMVAR) modeling of cortical field potentials, as an index for relating changes in large-scale neural activity to changes in cognitive state. We show that this stability measure can be used to decide the optimal window length for AMVAR modeling and to detect state transitions related to external sensory or motor events. By using this approach, we demonstrate clear differentiation of GO and NO-GO processes in a macaque monkey performing a visuomotor pattern discrimination task. Moreover, we are able to identify regional differences in state transitions, apparently reflecting regional information processing differences.

Instantaneous frequency estimation of nonlinear frequency-modulated signals in the presence of multiplicative and additive noise

This paper addresses the problem of estimating the instantaneous frequency (IF) of monocomponent nonlinear, not necessarily polynomial, frequency modulated (FM) signals affected by stationary multiplicative and additive noise. Both noise processes are assumed to be complex circular Gaussian and independent. The peak of the polynomial Wigner-Ville distribution (PWVD) is proposed here as an IF estimator. We derive analytical expressions for the bias and asymptotic variance of the estimator and propose an algorithm to select the optimal window length to resolve the bias-variance tradeoff in the IF estimation. Simulation results are presented to confirm the theoretical results.

Adaptive noise energy estimation in pathological speech signals

For pathological voices, spectral noise is closely related to the degree of perceived hoarseness. In this paper, noise variations are tracked during an utterance by means of an adaptive version of the normalized noise energy method [1]. A first step is devoted to pitch estimation, which allows defining the varying optimal time window length for noise retrieval, avoiding empty "dip" regions. The approach is tested on synthetic data and applied to real data coming from cordectomised adult male patients.

Instantaneous frequency estimation using higher order L-Wigner distributions with data-driven order and window length

The L-Wigner distributions are defined in order to improve the concentration of signal's time-frequency representation. For a finite distribution order and nonlinear instantaneous frequency (IF) it gives biased IF estimates. In the case of noisy signals the optimal window length and distribution order depend on the noise variance and unknown IF. In this article an adaptive IF estimator with the time-varying and data-driven window length and distribution order is developed. Based on the analysis that has been done here, lower order time-frequency distributions are introduced.