Rui J. P. de Figueiredo

A New Framework and Computer Program for Quantitative EMG Signal Analysis

Techniques for analyzing electromyographic signals, which estimate and detect potentials caused by active motor units in human striated muscles, are described. A framework within which these techniques are incorporated into a computer program for the quantitative analysis of EMG signals is then proposed. The resulting program allows the diagnosis of neurogenic and myogenic diseases by analyzing the waveforms of the motor unit potentials (MUPs). It also permits the research of the healthy and disturbed neuromuscular control loop by analyzing the point processes given by the activation of the single motor units.

Separation of superimposed signals by a cross-correlation method

An approach is presented for separating a superposition of delayed finite-duration signals, with unknown gains and delays, which overlap both in the time and frequency domains. The method is partly based on the cross-correlations among the signals and some of their derivatives. Given the data, an initial detection scheme formulates hypotheses on signals which may be present in the mixture, and provides estimates of the signal positions for each hypothesis. In the second stage, the most likely hypotheses are selected and accurate values of the signal amplitudes and their time positions are determined by a nonlinear least squares approach. The method is illustrated by a simulation with myoelectric (EMG) signals.

An Algorithm for Sequential Signal Estimation and System Identification for EMG Signals

This paper presents a new algorithm for optimal adaptation of the signal templates of a matched filter bank used in the detection of the motor unit action potential waveforms (abbreviated as MUAPs) in an electromyogram (EMG). It is of interest, for clinical diagnosis and therapy, to detect as many MUAPs as possible in a single measurement, and to determine for each motor unit the repetition. rate of its respective MUAP. For this purpose, we have developed a computer program which, in addition to other subprograms, contains the adaptive filter bank mentioned above. The templates in this fllter bank have to be adapted to nonpredetermined changes in measurement conditions such as the movement of the needle electrode inserted in the muscle. In the present paper, the above templates are estimated by means of a tumbling algorithm, so called because the successive MUAPs from a given motor unit are used as noisy data vectors in a time-varying Kalman filter-predictor framework, which alternately estinates their evolving shapes and identifies the time-varying parameters of the model generating them. The algorithm has been applied with success to synthetic and real EMG data.

Waveform Feature Extraction Based on Tauberian Approximation

A technique is presented for feature extraction of a waveform y based on its Tauberian approximation, that is, on the approximation of y by a linear combination of appropriately delayed versions of a single basis function x, i.e., y(t) = ¿M i = 1 aix(t - ¿i), where the coefficients ai and the delays ¿i are adjustable parameters. Considerations in the choice or design of the basis function x are given. The parameters ai and ¿i, i=1, . . . , M, are retrieved by application of a suitably adapted version of Pronys method to the Fourier transform of the above approximation of y. A subset of the parameters ai and ¿i, i = 1, . . . , M, is used to construct the feature vector, the value of which can be used in a classification algorithm. Application of this technique to the classification of wide bandwidth radar return signatures is presented. Computer simulations proved successful and are also discussed.

LM-g splines☆

Abstract As an extension of the notion of an L-g spline, three mathematical structures called LM-g splines of types I, II, and III are introduced. Each is defined in terms of two differential operators L = D n + ∑ j=0 n−1 a j (t)D j and M = ∑ i=0 m b i (t)D i , where n ⩾ m ges; 0, n > 0, D = d dt the coefficients aj, j = 0,…, n − 1, and bi, i = 0,…, m, are sufficiently smooth; and bm is bounded away from zero on [0, T]. Each of the above types of splines is the solution of an optimization problem more general than the one used in the definition of the L-g spline and hence it is recognized as an entity which is distinct from and more general mathematically than the L-g spline. The LM-g splines introduced here reduce to an L-g spline in the special case in which m = 0 and b0 = constant ≠ 0. After the existence and uniqueness conditions, characterization, and best approximation properties for the proposed splines are obtained in an appropriate reproducing kernel Hilbert space framework, their usefulness in extending the range of applicability of spline theory to problems in estimation, optimal control, and digital signal processing are indicated. Also, as an extension of recent results in the generalized spline literature, state variable models for the LM-g splines introduced here are exhibited, based on which existing least squares algorithms can be used for the recursive calculation of these splines from the data.

Canonical sound speed profile for the Central Bay of Bengal

Following Munks canonical theory, an algorithm has been presented for computing sound channel parameters in the western and southern Bay of Bengal. The estimated canonical sound speed profile using these parameters has been compared with computed values for a set of CTD and hydrocast data. The analysis indicates appreciable variation in the perturbation coefficient ε even over short ranges, particularly in the eastern region. This has an important implication in ray tracing, where the range dependency of the acoustic field can be introduced with suitable modification. In the region where the channel axis is nearly symmetrical about the upper and lower bound, the canonical profile almost reproduces the computed one. The results of the exponential, stratified model lead to a reasonable/realistic fit with the ocean beneath the thermocline.

Approximation-theoretic methods for nonlinear deconvolution and inversion

Abstract Nonlinear deconvolution and nonlinear inversion are cast as inverse problems in generalized Fock spaces. Generalized Fock spaces, introduced by de Figueiredo and Dwyer in [1], are reproducing kernel Hilbert spaces (RKHSs) of input-output maps represented by Volterra series equipped with an appropriately weighted inner product, the choice of the weights in the inner product depending on the particular problem under consideration. The solution to the nonlinear deconvolution problem presented here is the same as the one obtained previously for the nonlinear system identification problem [1–4]. However, the present solution to the nonlinear inversion problem consists of a new approach, whereby the unknown samples of the input are obtained from the given samples of the output by means of an efficient sequential algorithm. The algorithm is based on a framework which interpolates the input samples by an appropriate spline, and its sequential nature is elicited by the use of a truncated function basis to represent the spline.

An Image Transform Coding Scheme Based on Spatial Domain Considerations

Image transform coding is first briefly reviewed using conventional viewpoints. Then a new spatial domain interpretation is given to image transform coding. An improvement based on this viewpoint for the Fourier transform coding, which possesses simple spatial domain relations, is presented.

An Optimization Framework for Nonlinear Control Systems Design based on Multi-Constraints and Multi-Criteria

A survey of the authors recent contributions are given to a new multi-constrained and multi-criteria optimization approach to the design of optimal compensators for general MIMO nonlinear feedback control systems in several practical considerations including such as robust stabilization with the presence of uncertainty, tracking and model matching, and disturbance rejection problems. First, the general framework for nonlinear closed-loop feedback systems is described in a Banach space setting in the time domain. Then, several typical optimal feedback design problems are formulated. Moreover, existence, uniqueness and characteristics theorems are established. Finally, a convergent recursive algorithm for solving the general constrained optimization is included.

Localization performance measure and optimal edge detection

Recent developments in edge detection have exposed diiferent criteria to gauge the performance of edge detectors in the presense of noise. One of the criteria is Localization, which is the ability of the edge detector to produce from noisy data a detected edge that is as close as possible to the true edge in the image. In this paper, we show the limitation of the localization criteria as previously formulated and propose an alternative. This new performance measure is based on the theory of zero-crossings of stochastic processes. We show that the derivative of a Gaussian is the optimal edge detector for this new measure.