Abstract: An incoming wave number estimation device for receiving incoming radio waves by an array antenna in which a plurality (=M) of antenna elements are linearly arrayed with a same element spacing, and estimating the number of the incoming radio waves, including: a correlation matrix creation section for removing a diagonal element from a predetermined row or column constituting an M×M array covariance matrix, and creating a correlation matrix by extracting a predetermined p number of correlations from (M?1) number of correlations after the diagonal element is removed while sequentially shifting one element at a time, and arraying the p number correlations in a matrix; an estimation matrix creation section for creating an estimation matrix for estimating the incoming wave number using the correlation matrix; a QR decomposition section for performing QR decomposition on the estimation matrix; and an incoming wave number determination section for determining the number of incoming radio waves based on each row eleme

Abstract: A system and method for monitoring and fault detection in dynamic systems. A “cross-covariance” matrix is used to construct and implement a principle component analysis (PCA) model and/or partial least squares (PLS) model. This system is further utilized for monitoring and detecting faults in a dynamic system. Time series information is synchronized, with respect to a set of training data. Based on historical data, consistency of correlations between variables can be checked with respect to a given time stamp.

Abstract: The present invention relates to a method and system for processing time series signal data or image signal data indicative of a characteristic of an object. Received signal data are transformed into second signal data within a Stockwell domain based upon a sparse approximation of a S-transform of the signal data. The second signal data are then processed within the Stockwell domain to extract features therefrom. The processing includes determination of local spectra at predetermined locations; determination of voices at predetermined frequencies; and filtering of the signal data using a filter function in dependence upon frequency and time or space. The signal processing method and system according to the invention enables signal processing based on the S-transform using a desktop computer or workstation.

Abstract: In an environment of temporally and spatially uncorrelated white additive noise, the direction estimation apparatus for coherent signals calculates (M?1) instantaneous cross-correlations between some array data, and selecting multiple pairs each of which is consisted of p instantaneous correlations from the (M?1) instantaneous cross-correlations to form a Hankel correlation matrix. Next, the apparatus divides that Hankel matrix into an upper submatrix and a lower submatrix and then calculates a linear operator at time n by using the adaptive LMS algorithm with a fixed or time-varying step-size parameter and or using the adaptive NLMS algorithm from the two submatrices. Then a noise subspace is estimated from that linear operator. Finally the directions of incident signals at time n is estimated and tracked by using that noise subspace with Newton approximation.

Abstract: A process for extracting at least one variable associated with a periodic signal (S, S?) including a possible continuous component, a sinusoidal fundamental component and possible harmonics. Numerical samples of the periodic signal (S, S?) are formed and special filtering is applied to monitoring of the periodic signal. Each sample is interpreted as the sum of the fundamental component and the possible continuous component of this periodic signal. This process can be applied to evaluation of the torsion of a sidewall (11) of a tire (1) fitted on a wheel under the action of torque exerted between the rim (4) of this wheel and the tread (12) of the tire (1).

Abstract: A matrix includes samples associated with a first signal and samples associated with a second signal. The second signal includes a first portion associated with the first signal and a second portion associated with at least one disturbance, such as white noise or colored noise. A projection of the matrix is produced using canonical QR-decomposition. Canonical QR-decomposition of the matrix produces an orthogonal matrix and an upper triangular matrix, where each value in the diagonal of the upper triangular matrix is greater than or equal to zero. The projection at least substantially separates the first portion of the second signal from the second portion of the second signal.

Abstract: A system and method is disclosed for breaking a feedback loop by replacing at least one component in the feedback loop with a model containing two physically disconnected subnetworks that have terminals that are connected to ground with voltage controlled, voltage sources (VCVSs). Dependent source parameters of the VCVSs control lateral signal transfer though the model allowing the feedback loop to be opened or closed. The model maybe used in a software simulation in which a replicate circuit is used to set and maintain a closed-loop bias on the open-loop circuit. Small-signal analysis of the equivalent open-loop circuit allows extraction of transfer functions that yield a return ratio RR(s) corresponding to the modeled component.

Abstract: A communications device includes an antenna array for receiving different summations of source signals from a plurality of signal sources, a receiver coupled to the antenna array for receiving the different summations of source signals, and a signal separation processor coupled to the receiver. Processing by the signal separation processor includes creating a matrix based upon the different summations of source signals, with the matrix being defined by linear independent equations with fewer equations than unknowns. The matrix is underdetermined, and parameters associated with the matrix are modified based upon different sets of parameter values, and respective matrix quality factors associated with the different sets of parameter values are determined. The matrix is then biased with a preferred set of parameter values so that the solution space may be narrowed for obtaining a solution.

Abstract: The present invention relates to a method for recovering target speech from mixed signals, which include the target speech and noise observed in a real-world environment, based on split spectra using sound sources' locational information.

Abstract: A method of strongly decorrelating signals comprising processing input signals to determine delay and rotation parameters which implement at least one elementary paraunitary matrix. The parameters transform the input signals into output signals with improvement in a measure of strong decorrelation. The improvement in the measure of strong decorrelation is then assessed: if it is significant the latest output signals are, designated as input signals and the process is iterated. Iteration continues until the measure of strong decorrelation ceases to improve significantly, at which point the latest output signals are designated as signals decorrelated in a wide sense.

Abstract: Disclosed are a method and system for predicting future values of a target metric associated with a task executed on a computer system. The method comprises the steps of, over a given period of time, measuring at least one defined metric, transforming that measurement into a value for a predictor source metric, and using the value for the predictor source metric to obtain a predicted future value for said target metric. The preferred embodiment of this invention provides a flexible performance multi-predictor to solve the problem of providing accurate future behavior predictions for adaptive reconfiguration systems. The multi-predictor makes predictions about future workload characteristic by periodically reading available hardware counters. Also disclosed is a method and system for periodically reconfiguring an adaptive computer system by rescheduling tasks based on future behavior predictions.

Abstract: An auto-learned hierarchy algorithm that learns the hierarchical layout of a power monitoring system. Historical power data from each meter is received and placed into a data table. The main is assumed to be at the top of the hierarchy and is designated as the reference. A check matrix is developed indicating whether a possible connection exists between each meter pair combination. A correlation coefficient matrix (CCM) is calculated based on the data table, and entries in which no connection is possible are zeroed. The column for the reference meter from the CCM is copied to a correlation reference array (CRA), and the meter having the highest correlation with the reference meter in the CRA is marked as connected to the reference meter in a connection table. That meter's power is subtracted from the data table and the procedure is repeated until all meters have been analyzed.

Abstract: A method for use with equipment having filters, the method characterized by multiplying a matrix having a specified cut-boost setting of a filter of a graphic equalizer by a correction matrix to create a matrix having a corrected cut-boost setting of the filter of the graphic equalizer; adjusting an actual cut-boost setting of the filter of the graphic equalizer to be substantially equal to the corrected cut-boost setting of the filter of the graphic equalizer; and configuring the filter to have a Q value substantially equal to a linearizing Q value. In addition to the foregoing, other method embodiments are described in the claims, drawings, and text forming a part of the present application.

Abstract: Systems and methods are provided for directionally filtering signals by projecting a received signal onto a subspace substantially orthogonal to selected interfering signals. The received signal typically comprises at least one signal of interest, at least one selected interfering signal, and noise. The received signal may further comprise other signals, including non-selected interfering signals. The projection of the received signal results in substantially no contribution from the selected interference signals on the signal of interest. For example, substantially no residual energy of the selected interference signals remains as an influence on the signal of interest. In one embodiment, a system generates a converted matrix having a substantially orthogonal set of vectors. Each vector may represent one or more selected interfering signals. The vectors may comprise code characteristics of the selected interfering signals. A directional filter uses the matrix to perform the projection.

Abstract: Systems and methods are provided for monitoring, diagnosis and condition-based maintenance of mechanical systems. The disclosed systems and methods employ intelligent model-based diagnostic methodologies to effectuate such monitoring, diagnosis and maintenance. According to exemplary embodiments of the present disclosure, the intelligent model-based diagnostic methodologies combine or integrate quantitative (analytical) models and graph-based dependency models to enhance diagnostic performance. The disclosed systems and methods may be employed a wide variety of applications, including automotive, aircraft, power systems, manufacturing systems, chemical processes and systems, transportation systems, and industrial machines/equipment.

Abstract: A system and method for detecting erosion in turbine engine blades is provided. The blade erosion detection system includes a sensor data processor and a cluster analysis mechanism. The sensor data processor receives engine sensor data, including exhaust gas temperature (EGT) data, and augments the sensor data to determine sensor data residual values and the rate of change of the sensor data residual values. The augmented sensor data is passed to the cluster analysis mechanism. The cluster analysis mechanism analyzes the augmented sensor data to determine the likelihood that compressor blade erosion has occurred. Specifically, the cluster analysis mechanism performs a 2-tuple cluster feature analysis using Gaussian density functions that provide approximations of normal and eroded blades in a turbine engine. The 2-tuple cluster feature analysis thus provides the probability that the sensor data indicates erosion has occurred in the turbine engine.

Abstract: The diagnosis problem arises when a system's actual behavior contradicts the expected behavior, thereby exhibiting symptoms (a collection of conflict sets). System diagnosis is then the task of identifying faulty components that are responsible for anomalous behavior. To solve the diagnosis problem, the present invention describes a method for finding the minimal set of faulty components (minimal diagnosis set) that explain the conflict sets. The method includes acts of creating a matrix of the collection of conflict sets, and then creating nodes from the matrix such that each node is a node in a search tree. A determination is made as to whether each node is a leaf node or has any children nodes. If any given node has children nodes, then the node is split until all nodes are leaf nodes. Information gathered from the leaf nodes is used to determine the minimal diagnosis set.

Abstract: An analyzing method and system includes projecting light onto a specimen, detecting an optical spectrum from the specimen, dividing the detected optical spectrum by a predetermined time interval, applying a weighting vector and a gain and offset vector to the divided spectra to generate a resolution vector, quantizing an analog signal of the resolution vector to a digital signal, and applying a synthesis vector to the quantized spectra to restore the quantized spectra to a size of the optical spectrum. A spectrum having a large amplitude difference is temporally divided and is analyzed by applying different resolutions to individual time intervals. Spectral portions of the spectrum having relatively small peak amplitudes are selected as a region of interest (ROI) to be modified.

Abstract: The present invention is to provide a system for measuring the similarity between protein profile matrices which is suitably used for predicting a protein three-dimensional structure.

Abstract: A computer-based method for generating a scanning program for a stand-alone measuring equipment is provided. The method includes the steps of: receiving parameters, the parameters including output types of probing points; calculating a probing point coordinate multidimensional array; creating probing features; generating 3D program of each probing feature, and forming a control file by assimilating all 3D programs; and transferring the control file to a computer in the measuring equipment and executing the control file by utilizing measuring software in the computer to measure a workpiece. A related system is also provided.

Abstract: Measured values obtained in a measuring machine to be estimated are provided to estimate errors in the measured values. Based on the estimated errors in the measured values, a covariance matrix or correlation matrix of measured values is derived. The covariance matrix or correlation matrix is then subjected to eigenvalue decomposition to derive eigenvalues and eigenvectors. A normal random number with an expected value of 0 and a variance equal to an eigenvalue corresponding to the eigenvalue is generated as a coefficient of coupling for each eigenvector, and all eigenvectors are linearly coupled to generate pseudo-measured values of the measuring machine. The generated pseudo-measured values are subjected to statistic processing to estimate uncertainty of the measuring machine.

Abstract: A method of representing a sound field includes the steps of acquiring measurement signals (cn) which are delivered by simple sensors (2n) that are exposed to sound field (P) determining encoding filters which are representative of at least the structural characteristics of the sensors and processing the measurement signals (cn) by applying the encoding filters to the signals (cn), in order to determine a finite number of representative coefficients over time and in the three-dimensional space of the sound field (P).

Abstract: Systems methods and recordable media for predicting multi-variable outcomes based on multi-variable inputs. Additionally, the models described can be used to predict the multi-variable inputs themselves, based on the multi-variable inputs, providing a smoothing function, acting as a noise filter. Both multi-variable inputs and multi-variable outputs may be simultaneously predicted, based upon the multi-variable inputs. The models find a critical subset of data points, or “tent poles” to optimally model all outcome variables simultaneously to leverage communalities among outcomes.

Abstract: A signal processing method is disclosed, where, after inputting a measurement data weighted-spline filter formula is selected to calculate an initial value of a spline filter, weight is adjusted, spline filter output is calculated, convergence is judged thereafter. When the weight is not judged converged, the weight is updated and the weight adjusting and spline filter output calculation are repeated, to conduct a robust spline filtering on the measurement data.

Abstract: Systems and methods for the design or implementation of statistical filters for use in the spectral shaping of transmissions are disclosed. A desired power spectrum may be mapped to find pole locations that approximate the desired spectrum. These pole locations may then be mapped to the edge or inside of an equilateral polygon lying inside a unit circle, the equilateral polygon having the same number of sides as the order of the statistical filter desired and one vertex mapped to unity, to yield a set of eigenvalues. These eigenvalues may be the eigenvalues of a stochastic matrix the elements of which may be the Markov transition probabilities for use in a statistical filter designed to achieve the desired power spectrum. Use of a statistical filter employing these Markov transition values may be utilized to shape UWB or other signals to achieve the desired power spectrum.

Abstract: A parameter of a fluid passing through a pipe is measured using a spatial array of sensors disposed at different axial locations along the pipe. The spatial array includes at least two overlapping sub-arrays. Using the pressure signals, a signal processor determines a spatial correlation matrix for each of the sub arrays. The spatial correlation matrices from the sub-arrays are averaged, and the averaged spatial correlation matrix is used as input to an adaptive array processing algorithm. The pipe may be open ended such that it can be positioned within the fluid flow for forming a portion of a sensing device.

Abstract: Computer-implemented systems and methods for analyzing time series data. Statistical techniques are performed upon candidate autoregressive components and regressor components using the time series data. Autoregressive and regressor components are included in a predictive model based upon the autoregressive and regressor components' significance levels as determined by the statistical techniques.

Abstract: An engine diagnostic system is provided that enables a service technician to evaluate engine cylinder contribution to output power. The service technician couples one or more signal leads to the vehicle's battery, alternator, or accessory receptacle (e.g., cigarette lighter receptacle) to provide an alternator output signal to a signal analyzer. The signal analyzer processes the alternator output signal to generate an engine signature, which represents engine cylinder contribution to engine output power.

Abstract: An electromagnetic field analyzer includes a division-into-element portion that divides form data as an analysis object into coarse elements and fine elements. A prolongation matrix forming portion forms a prolongation matrix defining an electromagnetic field vector of the coarse elements divided by the division-into-element portion related to an electromagnetic field vector of the fine elements. Then, an approximate value calculation portion and an approximate solution correction portion calculate an approximate solution of the electromagnetic field vector of the fine elements by applying an iteration method of simultaneous linear equations while referring to the prolongation matrix. Accordingly, it becomes possible to perform an electromagnetic field analysis at high speed by using a multi-grid method using a non-nested mesh.

Abstract: A system and method for calibrating a multi-port S-parameter measurement device reduces the number of full calibrations necessary to characterize the multi-port S-parameter measurement device by utilizing a reciprocal network concept. The multi-port S-parameter measurement device includes a network analyzer having network ports connected to respective sets of switch ports on a switch. Full calibrations are performed on selected port pairs of the switch to determine the calibration arrays for each of the port pairs. Each port pair includes one switch port from two different sets of switch ports. A switch error having three switch error terms attributable to a reciprocal network introduced by an unselected one of the switch ports not included within any of the one or more port pairs is determined, and the switch error is de-embedded from the calibration arrays to construct a complete set of calibration arrays for all of the measurement paths in the multi-port S-parameter measurement device.

Abstract: A matrix reordering method performs reordering of elements of a coefficient matrix created based on coefficients of linear simultaneous equations whose solutions are to be produced by parallel processing of processors of a computer in accordance with Gaussian elimination. Herein, degrees corresponding to numbers of non-zero elements are calculated with respect to all pivots included in the coefficient matrix. Then, a first pivot whose degree is under a threshold (mindeg+?) is selected from among the pivots of the coefficient matrix, while a second pivot whose critical path length is minimum is also selected from among the pivots of the coefficient matrix. Replacement of elements is performed between the first pivot and second pivot to complete reordering with respect to the first pivot. In addition, non-zero elements, which are newly produced by the Gaussian elimination of the first pivot, are added to the coefficient matrix.

Abstract: A method for the blind identification of sources within a system having P sources and N receivers comprises at least one step for the identification of the matrix of the direction vectors of the sources from the information proper to the direction vectors ap of the sources contained redundantly in the m=2q order circular statistics of the vector of the observations received by the N receivers. Application to a communications network.

Abstract: A description is given of a method for the analysis and/or monitoring of the partial discharge behavior of an electrical operating means, in particular in terms of its development over time. Here, appropriate partial discharge data is recorded in process state matrices (2, 3), in which, in each case in a matrix element (5) of the process state matrix (1), the amplitude (7) of a partial discharge, its phase angle (6) and its frequency of occurrence is depicted (in particular what is known as a PRPD representation). A simplified analysis is made possible by the fact that, at a first time, a partial discharge process state is registered in a first process state matrix (2) and, at a later time, a further partial discharge process state is registered in a further process state matrix (3). Then, for the purpose of analysis and/or monitoring, the first (2) and the second (3) process state matrix are compared with the aid of comparison and scaling methods.

Abstract: Disclosed are a method and system for predicting future values of a target metric associated with a task executed on a computer system. The method includes the steps of, over a given period of time, measuring at least one defined metric, transforming that measurement into a value for a predictor source metric, and using the value for the predictor source metric to obtain a predicted future value for said target metric. The preferred embodiment of this invention provides a flexible performance multi-predictor to solve the problem of providing accurate future behavior predictions for adaptive reconfiguration systems. The multi-predictor makes predictions about future workload characteristic by periodically reading available hardware counters. Also disclosed is a method and system for periodically reconfiguring an adaptive computer system by rescheduling tasks based on future behavior predictions.

Abstract: Methods, systems and computer readable media for imposing monotonic consistency among results of multiple platforms measuring the same specific property for the same/equivalent series of samples, to provide viable comparisons of sensitivity and precision among the platforms as well as provide useful conversion formulas among the platforms to ensure equivalent quantitation.

Abstract: What is disclosed is a method for maintaining consistent color output across printers even when the inline sensors have differences in accuracy due to various technical and environmental factors. A spectrophotometer is used to measure the color quality of printed references. Adjustments are then iteratively made until reference charts of desired color quality are obtained. The printed reference allows one to achieve relatively high system performance by removing sensor inaccuracies. Using the printed reference measured by the inline sensor control systems of each machine are calibrated. At customer sites and at suitable intervals, a reference document can be read using the inline sensor on a reference machine and any differences from expected values can be calibrated out.

Abstract: An extended partial least squares (EPLS) approach for the condition monitoring of industrial processes is described. This EPLS approach provides two statistical monitoring charts to detect abnormal process behaviour as well as contribution charts to diagnose this behaviour. A theoretical analysis of the EPLS monitoring charts is provided, together with two application studies to show that the EPLS approach is either more sensitive or provides easier interpretation than conventional PLS.

Abstract: A reference matrix contains valid measurements characterizing operation of a multivariate process (220). Modeling parameters of the reference matrix are derived (222–232). The final model parameters, balanced with respect to measuring and modeling uncertainties (232), are applied to model (204) a new set of measurements (200). If the new set has no faults (206) then all modeled values and modeling uncertainties (208) can be used to control the process (218). If the new set has only one fault (210) ten the modeled value and modeling uncertainty of the faulted measurement plus the measured values and measuring uncertainties of the unfaulted measurements (212) can be used to control the process (218) while repair procedures are implemented for the identified fault (216). If the new set has more than one fault (214) then the process (218) should be shut down, and repair procedures should be implemented (216) for all identified faults.

Abstract: A synchronous vector measuring device can measure an absolute phase angle of a synchronous vector excellent in continuous numerical stability at high speed and with high accuracy in a noisy electric power system. A voltage measuring part measures the voltage of the electric power system at a period equal to 1/4N (N being a positive integer) of one period of a reference wave. A voltage root-mean-square value calculation part calculates, at each voltage measuring timing, a voltage root-mean-square value at a specific timing from the voltages measured at past 4N timings including the specific timing. An absolute phase angle calculation part makes, at each voltage measuring timing, an inverse cosine of a value obtained by dividing the voltage measured at the specific timing by the product of the voltage root-mean-square value and the square root of 2, as the absolute phase angle of the synchronous vector at the specific timing.

Abstract: In a method for reducing sensed physical variables generating a plurality of control commands are generated at a control rate as a function of the sensed physical variables. An estimate of a relationship between the sensed physical variables and the control commands is also is used in generating the plurality of control commands. The estimate of the relationship is updated based upon a response by the sensed physical variables to the control commands. The generation of the control commands involves a quadratic dependency on the estimate of the relationship and the quadratic dependency is updated based on the update to the estimate.

Abstract: A computer implemented method on a computer readable media is provided for determining the source of a problem in a complex system of managed components based upon symptoms. The problem source identification process is split into different activities. Explicit configuration non-specific representations of types of managed components, their problems, symptoms and the relations along which the problems or symptoms propagate are created that can be manipulated by executable computer code. A data structure is produced for determining the source of a problem by combining one or more of the representations based on information of specific instances of managed components in the system. Computer code is then executed which uses the data structure to determine the source of the problem from one or more symptoms.

Abstract: Embodiments of a system and method are disclosed that exploit the unique higher order statistics of temporally dependent waveforms to detect and enumerate signals in a multi-signal and noise environment. The embodiments use spatial 4th-order cumulants or spatial 2nd-order moments in a Blind Source Separation operation and generalized eigenvalue decomposition to determine unique matrix pencil eigenvalues for a set of unknown signals. Sequential detection in the complex plane of the eigenvalues in associated tracks for successive blocks of sensor data serve as the basis of the detection decision. The embodiments may include a multi-element array and do not require a priori knowledge of the signal environment to detect and enumerate the signals.

Abstract: Methods, systems and computer readable media for imposing monotonic consistency among results of multiple platforms measuring the same specific property for the same/equivalent series of samples, to provide viable comparisons of sensitivity and precision among the platforms as well as provide useful conversion formulas among the platforms to ensure equivalent quantitation.

Abstract: In an ensemble oscillator system including multiple free-running oscillators, a voltage controlled oscillator having a frequency responsive to a control signal, and a differencer unit that measures time differences between the oscillators, an adaptive Kalman Filter Processor (AKFP) generates the control signal responsive to the time differences. The AKFP uses oscillator noise models to model noise/errors of the ensemble system oscillators, including random noise parameters, and adaptively estimates the errors and the random noise parameters to derive the control signal.

Abstract: A method of estimating a pure spectrum and a concentration of each component constituting n sample mixtures, in which p kinds of components are mixed, includes (a) performing a principal component analysis of the spectra of the n mixtures, which are measured using m wavelengths, to represent the spectra of the n mixtures as factors and scores of the respective factors, wherein n, p, and m are integers and m>p, and (b) performing an independent component analysis of the scores obtained in (a) to estimate the pure spectra and the concentrations of the respective components.

Abstract: Signals are separated by introducing a function having a monotonously increasing characteristic like an exponential type function as a cost function, and applying an adaptive algorithm that minimizes that cost function in terms of a signal separation matrix. That is, there is provided a signal processing apparatus that separates and outputs an original signal from the observed signal x(t), in which multiple multidimensional signals are mixed, wherein the nonlinear function 21 is operated on an input observed signal x(t) and an estimated separation matrix W(t?1) estimated at a previous cycle. Then, an error signal e(t) is calculated 22 based on y(t) formed by this nonlinear function 21, the estimated separation matrix W(t?1) estimated at the previous cycle, and the observed signal x(t) at that time.

Abstract: The aim of the present invention is to estimate EDR directions in a single index model composed of a large number of variables with simple calculations without using the inverse matrix of the variance-covariance matrix and principle component analysis. Data conversion means 21 receives, from an input device 3, data to be analyzed, the data composed of sets of response variables and explanatory variables, standardizes the explanatory variables, and sends them to slice average calculating means 22. The slice average calculating means 22 divides the data into two slices with reference to the median of the response variables to calculate the mean vector of the explanatory variables on a slice basis. The calculated mean vectors are sent to EDR direction calculating means 23. The EDR direction calculating means 23 calculates the difference between the mean vectors for respective slices to estimate an EDR direction.

Abstract: Disclosed herein is an apparatus and method of calibrating the parameters of a Viterbi detector 138 in which each branch metric is calculated based on noise statistics that depend on the signal hypothesis corresponding to the branch. An offline algorithm for calculating the parameters of data-dependent noise predictive filters 304A-D is presented which has two phases: a noise statistics estimation or training phase, and a filter calculation phase. During the training phase, products of pairs of noise samples are accumulated in order to estimate the noise correlations. Further, the results of the training phase are used to estimate how wide (in bits) the noise correlation accumulation registers need to be. The taps [t2[k], t1[k], t0[k]] of each FIR filter are calculated based on estimates of the entries of a 3-by-3 conditional noise correlation matrix C[k] defined by Cij[k]=E(ni?3nj?3|NRZ condition k).

Abstract: An apparatus and method is provided for efficiently determining the source of problems in a complex system based on observable events. By splitting the problem identification process into two separate activities of (1) generating efficient codes for problem identification and (2) decoding the problems at runtime, the efficiency of the problem identification process is significantly increased. Various embodiments of the invention contemplate creating a causality matrix which relates observable symptoms to likely problems in the system, reducing the causality matrix into a minimal codebook by eliminating redundant or unnecessary information, monitoring the observable symptoms, and decoding problems by comparing the observable symptoms against the minimal codebook using various best-fit approaches. The minimal codebook also identifies those observable symptoms for which the greatest benefit will be gained if they were monitored as compared to others.

Abstract: A novel method and apparatus is provided for enabling the computation of a signal in a certain subspace, its projection that lies outside the subspace, and the orthogonal basis for a given matrix. More particularly, the present invention relates to the use of such a method or apparatus for real-time hardware applications since the method and apparatus may be utilized without matrix inversions or square root computations.