Showing papers on "Wavelet published in 1979"
TL;DR: The l 1 norm can also be used to extract a wavelet w from a trace t when a spike train s is known as discussed by the authors, which can be constrained to give a smooth wavelet which integrates to zero and goes to zero at the ends.
Abstract: Given a wavelet w and a noisy trace t = s * w + n, an approximation s of the spike train s can be obtained using the l 1 norm. This extraction has the advantage of preserving isolated spikes in s. On some types of data the spike train s can represent s as a sparse series of spikes, which may be sampled at a rate higher than the sample rate of the data trace t. The extracted spike train s may be qualitatively much different than those commonly extracted using the l 2 norm.The l 1 norm can also be used to extract a wavelet w from a trace t when a spike train s is known. This wavelet extraction can be constrained to give a smooth wavelet which integrates to zero and goes to zero at the ends.Given a trace t and an initial approximation for either s or w, it is possible to alternately extract spike trains and wavelets to improve the representation of trace t.Although special algorithms have been developed to solve l 1 problems, all of the calculations can be performed using a general linear programming system. Proper weighting procedures allow these methods to be used on ungained data.
399 citations
TL;DR: Homomorphic analysis and pole-zero modeling of electrocardiogram (ECG) signals are presented and the pole- zero pattern of the models can give a clue to classify the normal and abnormal signals.
Abstract: Homomorphic analysis and pole-zero modeling of electrocardiogram (ECG) signals are presented in this paper. Four typical ECG signals are considered and deconvolved into their minimum and maximum phase components through cepstral filtering, with a view to study the possibility of more efficient feature selection from the component signals for diagnostic purposes. The complex cepstra of the signals are linearly filtered to extract the basic wavelet and the excitation function. The ECG signals are, in general, mixed phase and hence, exponential weighting is done to aid deconvolution of the signals. The basic wavelet for normal ECG approximates the action potential of the muscle fiber of the heart and the excitation function corresponds to the excitation pattern of the heart muscles during a cardiac cycle. The ECG signals and their components are pole-zero modeled and the pole-zero pattern of the models can give a clue to classify the normal and abnormal signals. Besides, storing only the parameters of the model can result in a data reduction of more than 3:1 for normal signals sampled at a moderate 128 samples/s.
45 citations
TL;DR: In this paper, the relationship between two finite difference schemes (15° and 40°) and the Kirchhoff summation approach is discussed by using closed form solutions of Claerbout's approximate versions of the wave equation.
Abstract: The relationship between two finite-difference schemes (15° and 40°) and the Kirchhoff summation approach is discussed by using closed form solutions of Claerbout's approximate versions of the wave equation. Forward extrapolation is presented as a spatial convolution procedure for each frequency component. It is shown that downward extrapolation can be considered as a wavelet deconvolution procedure, the spatial wavelet being given by the wave theory. Using this concept, a three-dimensional model for seismic data is proposed.
The advantages of downward extrapolation in the space-frequency domain are discussed.
Finally, it is derived that spatial sampling imposes an upper limit on the aperture and a lower limit on the extrapolation step.
37 citations
01 Jan 1979
TL;DR: The extraction and correction of the distorted seismic wavelet yields many interpretive advantages, such as log comparisons, line ties, fine stratigraphic definition, detection of thin layers, and data quality.
Abstract: The extraction and correction of the distorted seismic wavelet yields many interpretive advantages. Well log comparisons, line ties, fine stratigraphic definition, detection of thin layers, and data quality are all improved by successful wavelet processing.
3 citations
TL;DR: In this article, a multiply reflected ray can be decomposed into three wavelets that in turn can be used to construct synthetic seismograms for each of the ray turning points, corresponding to a source term and two terms that give the impulse response of the medium.
Abstract: Seismograms recorded at selected points along the travel path of a multiply reflected ray can be decomposed into three wavelets that in turn can be used to construct synthetic seismograms for each of the ray turning points The three wavelets correspond to a source term and two terms that give the impulse response of the medium The decomposion provides a direct source function estimate if the reflection and conversion coefficients can be determined for the depth at which the source is located Application of the process to the construction of synthetic seismograms is demonstrated