Elementary Waveform Research Articles

Parabolic dictionary learning for seismic wavefield reconstruction across the streamers

Dictionary learning (DL) methods are effective tools to automatically find a sparse representation of a data set. They train a set of basis vectors on the data to capture the morphology of the redundant signals. The basis vectors are called atoms, and the set is referred to as the dictionary. This dictionary can be used to represent the data in a sparse manner with a linear combination of a few of its atoms. In conventional DL, the atoms are unstructured and are only numerically defined over a grid that has the same sampling as the data. Consequently, the atoms are unknown away from this sampling grid, and a sparse representation of the data in the dictionary domain is not sufficient information to interpolate the data. To overcome this limitation, we have developed a DL method called parabolic DL, in which each learned atom is constrained to represent an elementary waveform that has a constant amplitude along a parabolic traveltime moveout. The parabolic structure is consistent with the physics inherent to the seismic wavefield and can be used to easily interpolate or extrapolate the atoms. Hence, we have developed a parabolic DL-based process to interpolate and regularize seismic data. Briefly, it consists of learning a parabolic dictionary from the data, finding a sparse representation of the data in the dictionary domain, interpolating the dictionary atoms over the desired grid, and, finally, taking the sparse representation of the data in the interpolated dictionary domain. We examine three characteristics of this method, i.e., the parabolic structure, the sparsity promotion, and the adaptation to the data, and we conclude that they strengthen robustness to noise and to aliasing and that they increase the accuracy of the interpolation. For both synthetic and field data sets, we have successful seismic wavefield reconstructions across the streamers for typical 3D acquisition geometries.

A Novel Zone Division Approach for Power System Fault Detection Using ANN-Based Pattern Recognition Technique

This paper presents a waveform analysis-based approach for detection and classification of short-circuit faults in large power networks. To reduce the computational burden in dealing with a large volume of waveform data, a novel zone detection method has been used where a large power network is divided into optimal number of zones with manageable number of buses and lines. A first module of the artificial neural network-based classifier has been developed to perform an “exploratory global search” to find the faulty zone, which is then refined to a “local search” within a zone, by a second module of classifier for determination of exact fault location and fault type. The elementary waveform data are being captured by disturbance recorders placed at strategic buses, termed as “monitoring locations.” Feature extraction, which is typically the underlying principle of any waveform analysis-based fault detection approach, is implemented by the extended Kalman filter. The proposed method has been successfully tested on the IEEE 57 bus network with encouraging results.

Normal needle electromyographic insertional activity morphology: a clinical and simulation study.

Needle electromyographic insertional activity waveform morphology, and mechanisms of generation, have received little attention. This study analyzes the individual component waveforms that contribute to the burst of electrical activity known as insertional activity. One hundred monopolar needle insertions were slowly performed and high speed recorded to allow better separation of the contributing individual component waveforms. Analysis of the many waveforms recorded demonstrates several classes of potentials. All of these could be reconstructed by the summation of two basic or elementary waveform patterns: a biphasic initially negative spike with or without a "prepotential" similar to an end-plate spike, and the biphasic initially positive spike with a slowly declining negative phase, similar to a positive sharp wave, though shorter in duration. The relationship between these elementary waveforms and their hypothesized generator sources is discussed.

An optimized time-frequency distribution for speech analysis

In order to analyse and interpret speech signals, different time-frequency representations are used (e.g. spectrogram, Wigner-Ville distribution, wavelets). In this paper we construct within Cohen's class of time-frequency distributions the distribution that is optimally suited for the representation of speech signals. Thereby we take advantage of the special time-frequency structure of speech expressed in the Elementary Waveform Speech Model (EWSM, d'Alessandro, 1990). As an application we present an algorithm that extracts a point pattern in the time-frequency plane out of the speech signal using the optimized distribution. Thus we get a very simple representation of the speech signal that is well interpretable both for non-stationary and for stationary speech segments. Furthermore this representation could serve as a base for further analysis (e.g classification).

Time-frequency speech transformation based on an elementary waveform representation

A representation of the speech signal as a sum of elementary waveforms (Elementary Waveform Speech Model or EWSM) is introduced and some of its features for modifying localized time-frequency events are demonstrated. The elementary waveforms model the local spectro-temporal maxima of energy within the speech signal thanks to the use of simple mathematical functions. An automatic analysis-synthesis system allows for waveforms parameters estimation, using frame-by-frame processing: spectral modelling and segmentation using short-time Fourier transform and LPC spectrum, Fourier filtering according to this segmentation, waveform spotting in each channel, waveform modelling using simple functions. The classical theory of speech production proves the validity of the EWSM parameters; their modifications yield well-localized time-frequency transformations, including frequency compression/expansion, pitch, formant and noise modification.

A practical prediction method using an elementary response wave form for the road traffic noise at a T-type intersection.

A practical prediction method using an elementary response wave form for the road traffic noise at a T-type intersection.

Basis functions for sinusoidal evoked potentials: A waveform analysis program on a small computer

A computer program for the PDP-12 is described that reduces a series of discrete time points representing an evoked potential to a set of fundamental waveform specifications in amplitude, latency, duration, etc., for principal potential deflections or waves. To derive a basis function the program assumes the evoked potential is sinusoidal and estimates coefficients to the elementary waveform: v(t)=v 0 sin (ωt + œ) e αt Data is read from LINC tape as single or double precision points, smoothed and displayed with a cursor, baseline, and cursor reference location. The program locates the zero-crossover and amplitude points in either an automatic mode or by operator interaction from the console keyboard. Advantages of the program over visual waveform analysis include: Rapid reduction of the complex waveform to a few characteristic parameters, convenience and numeric output for statistics and curve fitting. The program has general usefulness to data processing in the neurosciences.