Wavelet based analysis and characterization of the ECG signal.

doi:10.1080/0309190031000121532

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Wavelet based analysis and characterization of the ECG signal.

Journal Article•DOI•

Wavelet based analysis and characterization of the ECG signal.

M. J. Burke¹, Mohamed Nasor¹•Institutions (1)

Trinity College, Dublin¹

01 Mar 2004-Journal of Medical Engineering & Technology (Taylor & Francis)-Vol. 28, Iss: 2, pp 47-55

TL;DR: A wavelet analysis technique based on the Mexican Hat wavelet was used to identify the onset and termination points and the duration of the principal constituent components of the human electrocardiogram (ECG).

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Abstract: This paper reports the use of a wavelet analysis technique based on the Mexican Hat wavelet to identify the onset and termination points and the duration of the principal constituent components of the human electrocardiogram (ECG). ECG recordings were obtained from 21 healthy subjects aged between 13 and 65 years, over a wide range of heart rates extending from 46 to 184 beats min−1. A wavelet transform method was then used to locate precisely the positions of the onset, termination and the durations of individual components in the ECG. Component times were then classified according to the heart rate associated with the cardiac cycle to which the component belonged. Second order equations of the form were fitted to the data obtained for each component to characterize its timing variation.

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Journal Article•DOI•

Evaluation of real-time QRS detection algorithms in variable contexts.

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François Portet¹, Alfredo Hernandez², Guy Carrault²•Institutions (2)

Institut de Recherche en Informatique et Systèmes Aléatoires¹, University of Rennes²

01 May 2005-Medical & Biological Engineering & Computing

TL;DR: The results show that the evaluated detectors are indeed complementary, for example, the Pan-Tompkins detector is the best in most contexts but the Okada detector generates fewer errors in the presence of electrode motion artifact.

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Abstract: A method is presented to evaluate the detection performance of real-time QRS detection algorithms to propose a strategy for the adaptive selection of ORS detectors, in variable signal contexts. Signal contexts are defined as different combinations of QRS morphologies and clinical noise. Four QRS detectors are compared in these contexts by means of a multivariate analysis. This evaluation strategy is general and can be easily extended to a larger number of detectors. A set of morphology contexts, corresponding to eight QRS morphologies (normal, PVC, premature atrial beat, paced beat, LBBB, fusion, RBBB, junctional premature beat), was extracted from 17 standard ECG records. For each morphology context, the set of extracted beats, ranging from 30 to 23000, was resampled to generate 50 realisations of 20 concatenated beats. These realisations were then used as input to the QRS detectors, without noise, and with three different types of additive clinical noise (electrode motion artifact, muscle artifact, baseline wander) at three signal-to-noise ratios (5 dB, -5 dB, -15 dB). Performance was assessed by the number of errors, which reflected both false alarms and missed beats. The results show that the evaluated detectors are indeed complementary. For example, the Pan-Tompkins detector is the best in most contexts but the Okada detector generates fewer errors in the presence of electrode motion artifact. These results will be particularly useful to the development of a real-time system that will be able to choose the best ORS detector according to the current context.

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53 citations

Cites background or methods from "Wavelet based analysis and characte..."

..., 1999; DASKALOV and CHRISTOV, 1999) and axe still being proposed (BENITEZ et al., 2001; BURKE and NASOR, 2004; DOTSINSKY and STOYANOV, 2004)....
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..., 2001; BURKE and NASOR, 2004; DOTSINSKY and STOYANOV, 2004). As it would be impracticable to compare all of them, only four were selected according to these criteria: ability to work in real time, ease of implementation, robustness with respect to noise, and knowledge of their performance in noiseless situations. The four chosen detectors were those proposed by PaN and TOMPKINS (1985), GRITZALI (1988), FRADEN and NEWMAN (1980) and OKADA (1979)....
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..., 2001; BURKE and NASOR, 2004; DOTSINSKY and STOYANOV, 2004). As it would be impracticable to compare all of them, only four were selected according to these criteria: ability to work in real time, ease of implementation, robustness with respect to noise, and knowledge of their performance in noiseless situations. The four chosen detectors were those proposed by PaN and TOMPKINS (1985), GRITZALI (1988), FRADEN and NEWMAN (1980) and OKADA (1979). FREISEN et al. (1990) presented those of FRADEN and NEWMAN (1980) and OKADA (1979) as AF2 and DF2 in their study; they demonstrated that these detectors are sensitive to different types of noise and are, in this sense, complementary....
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...…1979; FRADEN and NEUMAN, 1980; PAN and TOMPKINS, 1985; GRITZALI, 1988; POLI et al., 1995; SILIPO and MARCHESI, 1998; KADAMBE et al., 1999; WIEBEN et al., 1999; DASKALOV and CHRISTOV 1999) and are still being proposed (BENITEZ et al., 2001; BURKE and NASOR, 2004; DOTSINSKY and STOYANOV, 2004)....
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...Even if the study is l imited to simple algorithms here, the method is general, and other detectors, such as those recently proposed (BENITEZ et al., 2001; BURKE and NASOR, 2004; DOTSINSKY and STOYANOV, 2004) and described by KOHLER et al....
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Journal Article•DOI•

Implementing Wavelets in Continuous-Time Analog Circuits With Dynamic Range Optimization

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Joël Karel¹, Sandro A. P. Haddad², Senad Hiseni³, Ronald L. Westra¹, Wouter A. Serdijn³, Ralf Peeters¹ - Show less +2 more•Institutions (3)

Maastricht University¹, University of Brasília², Delft University of Technology³

01 Feb 2012-IEEE Transactions on Circuits and Systems

TL;DR: A method is described to implement wavelets in analog circuits by fitting the impulse response of a linear system to the time-reversed wavelet function using an L2 criterion, which offers a large performance increase over previous Padé-based approaches.

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Abstract: Signal processing by means of analog circuits offers advantages from a power consumption viewpoint. A method is described to implement wavelets in analog circuits by fitting the impulse response of a linear system to the time-reversed wavelet function. The fitting is performed using local search involving an L2 criterion, starting from a deterministic starting point. This approach offers a large performance increase over previous Pade-based approaches and allows for the circuit implementation of a larger range of wavelet functions. Subsequently, using state-space optimization the dynamic range of the circuit is optimized. Finally, to illustrate the design procedure, a sixth-order L2-approximated orthonormal Gaussian wavelet filter using Gm-C integrators is presented.

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47 citations

Cites methods from "Wavelet based analysis and characte..."

...Finally, the intermediate order continuous-time model is reduced with a balance and truncate technique to a desired low order , typically between 3 and 15....
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Journal Article•DOI•

Analysis of Fractionated Atrial Fibrillation Electrograms by Wavelet Decomposition

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Richard P. M. Houben, Natasja M.S. de Groot¹, Maurits A. Allessie¹•Institutions (1)

Maastricht University¹

05 Feb 2010-IEEE Transactions on Biomedical Engineering

TL;DR: Wavelet transformation can be a useful technique to detect the primary potentials and quantify the degree of fractionation of fibrillation electrograms, which could enable real-time mapping of complex cases of human AF and classification of the underlying electropathological substrate.

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Abstract: This study introduces the use of wavelet decomposition of unipolar fibrillation electrograms for the automatic detection of local activation times during complex atrial fibrillation (AF). The purpose of this study was to evaluate this technique in patients with structural heart disease and longstanding persistent AF. In 46 patients undergoing cardiac surgery, unipolar fibrillation electrograms were recorded from the right atrium, using a mapping array of 244 electrodes. In 25 patients with normal sinus rhythm, AF was induced by rapid pacing, whereas 21 patients were in persistent AF. In patients with longstanding AF, the atrial electrograms showed a high degree of fractionation. In each patient, 12 s of AF were analyzed by wavelet transformation (15 scales). The finest scales (1-7) were used to reconstruct a “local” fibrillation electrogram, whereas with the coarse scales (9-15), a far-field signal was generated. With these local and far-field electrograms, the “primary” fibrillation potentials, due to wave propagation underneath the electrode, could be distinguished from double potentials and multiple components generated by remote wavefronts. Wavelet transformation resulted in AF histograms with a closely Gaussian distribution and the automatically generated activation maps showed a good resemblance with fibrillation maps obtained by laborious manual editing. A special chaining algorithm was developed to detect multiple components in fractionated electrograms. The degree of fractionation showed a positive correlation with the complexity of fibrillation, thus providing an objective quantification of the degree of electrical dissociation of the atria. Wavelet transformation can be a useful technique to detect the primary potentials and quantify the degree of fractionation of fibrillation electrograms. This could enable real-time mapping of complex cases of human AF and classification of the underlying electropathological substrate.

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44 citations

Proceedings Article•DOI•

Study on Wavelet Transform in the Processing for ECG Signals

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Yun-fu Tan¹, Lei Du¹•Institutions (1)

Yanshan University¹

19 May 2009

TL;DR: Wavelet Transform is used to filter out noise interferences of ECG signals for the above mentioned problem, and it has more obvious advantages more than traditional methods.

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Abstract: ECG signals often are mixed with the myo-electrical interference, the power frequency interference and the baseline drift, and traditional filtering methods have certain shortcomings, which badly impact on the detection and the analysis of ECG(Electrocardiogram) signals, so we use Wavelet Transform to filter out noise interferences of ECG signals for the above mentioned problem. Firstly, coif4 wavelet is adopted to scale decompose ECG signals containing noises, secondly, the soft and hard threshold value quantify high-frequency coefficients of every scale, finally, the wavelet reconstructs high-frequency coefficients of every scale which are quantified by the threshold value to get ECG signals being filtering. Experiments show that Wavelet Transform has well real-time and good filtering effect, and it has more obvious advantages more than traditional methods.

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24 citations

Journal Article•DOI•

An ECG simulator with a novel ECG profile for physiological signals.

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Jan-Christoph Edelmann¹, Dominik Mair¹, Daniel Ziesel¹, Martin Burtscher¹, Thomas Ussmueller¹ - Show less +1 more•Institutions (1)

University of Innsbruck¹

01 Oct 2018-Journal of Medical Engineering & Technology

TL;DR: A low-cost open-source electrocardiography (ECG) simulator comprising both MATLAB software for signal generation and a dedicated circuit board for signal output via a commercial sound card is introduced.

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Abstract: This work introduces a low-cost open-source electrocardiography (ECG) simulator comprising both MATLAB software for signal generation and a dedicated circuit board for signal output via a commercial sound card. Synthetic, rate-dependent ECG simulation is based on third-order polynomials that are calculated in sections for the main waves and spikes, respectively. Besides the heart rate, the output profile is fully adjustable with respect to Einthoven lead signals I-III, the amplitudes of the individual ECG waves and spikes, as well as the constitution and intensity of common distortions. The underlying coefficients for the synthetic ECG profile are obtained experimentally by analysing recordings of 22 healthy individuals with heart rates in the range of 40-180 bpm. Eight of these recordings are selected to determine the coefficients for the polynomials (training set) while the remaining 14 serve as test set to evaluate their applicability and accuracy. Thereby, a mean correlation of 98.57% is found which is superior in comparison with a widely accepted rate-dependent ECG profile that is generated from square root and linear terms (correlation score: 91.46%). Although other use-cases are feasible, the focus of this work is the development of an ECG simulator for academic research and university education. Both the MATLAB source code and the circuit layout files are available in the online supplement stimulating further work on this topic.

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13 citations

Cites background or methods from "Wavelet based analysis and characte..."

...Generating synthetic ECG signals requires the recreation of signal shapes with the principal structure depicted in Figure 1 [7]....
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...46% for the profile of Burke and Nasor [4,7]....
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...Determination of the accuracy between recorded ECG signals with the profiles of this work and the profile suggested by Burke & Nasor [4,7]....
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...As one can observe from the figures, the QRS-complex is barely changing with respect to HR which is not adequately considered in the widely accepted ECG profile of Burke and Nasor [4,7]....
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...%) compared to a widely used version introduced by Burke and Nasor (91.46%)....
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References

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Open Access

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Journal Article•DOI•

Singularity detection and processing with wavelets

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Stéphane Mallat¹, Wen-Liang Hwang¹•Institutions (1)

New York University¹

01 Mar 1992-IEEE Transactions on Information Theory

TL;DR: It is proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz exponents.

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Abstract: The mathematical characterization of singularities with Lipschitz exponents is reviewed. Theorems that estimate local Lipschitz exponents of functions from the evolution across scales of their wavelet transform are reviewed. It is then proven that the local maxima of the wavelet transform modulus detect the locations of irregular structures and provide numerical procedures to compute their Lipschitz exponents. The wavelet transform of singularities with fast oscillations has a particular behavior that is studied separately. The local frequency of such oscillations is measured from the wavelet transform modulus maxima. It has been shown numerically that one- and two-dimensional signals can be reconstructed, with a good approximation, from the local maxima of their wavelet transform modulus. As an application, an algorithm is developed that removes white noises from signals by analyzing the evolution of the wavelet transform maxima across scales. In two dimensions, the wavelet transform maxima indicate the location of edges in images. >

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4,064 citations

"Wavelet based analysis and characte..." refers background in this paper

...Mallat and Hwang [32] have shown that a singular behaviour, i.e. a distinct change in the profile of the signal s(t) at time to means that there exists a modulus maxima line which converges towards the point to on the time axis as a?...
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...Mallat and Hwang [32] have shown that a singular behaviour, i....
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...Although the precise locations in time of the modulus maxima associated with a particular feature vary across levels, they are always identified as the closest maxima points in time as the level increases [11, 31, 32]....
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Journal Article•DOI•

Decomposition of Hardy functions into square integrable wavelets of constant shape

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A. Grossmann, J. Morlet

01 Jul 1984-Siam Journal on Mathematical Analysis

TL;DR: In this article, the authors studied square integrable coefficients of an irreducible representation of the non-unimodular $ax + b$-group and obtained explicit expressions in the case of a particular analyzing family that plays a role analogous to coherent states (Gabor wavelets) in the usual $L_2 $ -theory.

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Abstract: An arbitrary square integrable real-valued function (or, equivalently, the associated Hardy function) can be conveniently analyzed into a suitable family of square integrable wavelets of constant shape, (i.e. obtained by shifts and dilations from any one of them.) The resulting integral transform is isometric and self-reciprocal if the wavelets satisfy an “admissibility condition” given here. Explicit expressions are obtained in the case of a particular analyzing family that plays a role analogous to that of coherent states (Gabor wavelets) in the usual $L_2 $ -theory. They are written in terms of a modified $\Gamma $-function that is introduced and studied. From the point of view of group theory, this paper is concerned with square integrable coefficients of an irreducible representation of the nonunimodular $ax + b$-group.

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3,423 citations

"Wavelet based analysis and characte..." refers background in this paper

...Grossman and Morlet [30] showed that better identification of distinct features in the signal could be obtained by the decomposition of each scale into several sub-scales or voices while maintaining octave scaling....
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Book•

Characterization of Signals From Multiscale Edges

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Stéphane Mallat¹, S. Zhong¹•Institutions (1)

New York University¹

11 Aug 2011

TL;DR: The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges and shows that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures.

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Abstract: A multiscale Canny edge detection is equivalent to finding the local maxima of a wavelet transform. The authors study the properties of multiscale edges through the wavelet theory. For pattern recognition, one often needs to discriminate different types of edges. They show that the evolution of wavelet local maxima across scales characterize the local shape of irregular structures. Numerical descriptors of edge types are derived. The completeness of a multiscale edge representation is also studied. The authors describe an algorithm that reconstructs a close approximation of 1-D and 2-D signals from their multiscale edges. For images, the reconstruction errors are below visual sensitivity. As an application, a compact image coding algorithm that selects important edges and compresses the image data by factors over 30 has been implemented. >

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3,187 citations

"Wavelet based analysis and characte..." refers background in this paper

...Although the precise locations in time of the modulus maxima associated with a particular feature vary across levels, they are always identified as the closest maxima points in time as the level increases [11, 31, 32]....
[...]

Journal Article•DOI•

Time/frequency mapping of the heart rate, blood pressure and respiratory signals.

[...]

Peter Novak¹, Vera Novak¹•Institutions (1)

Université de Montréal¹

01 Mar 1993-Medical & Biological Engineering & Computing

TL;DR: The discrete Wigner distribution was implemented for the time/frequency mapping of variations of R-R interval, blood pressure and respiratory signals and it was shown that the DWD follows well the instantaneous changes of spectral content of cardiovascular and respiratory messages which characterise the dynamics of autonomic nervous system responses.

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Abstract: The discrete Wigner distribution (DWD) was implemented for the time/frequency mapping of variations of R-R interval, blood pressure and respiratory signals. The smoothed cross-DWD was defined and the modified algorithm for the smoothed auto- and cross-DWD was proposed. Spurious cross-terms were suppressed using a smoothing data window and a Gauss frequency window. The DWD is easy to implement using the FFT algorithm. Examples show that the DWD follows well the instantaneous changes of spectral content of cardiovascular and respiratory signals which characterise the dynamics of autonomic nervous system responses.

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176 citations

Journal Article•DOI•

The normal Q-T interval.

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Ernst Simonson¹, Lee D. Cady², Max A. Woodbury²•Institutions (2)

University of Minnesota¹, New York University²

01 Jun 1962-American Heart Journal

TL;DR: The normal limits of the Q-T interval are presented in five ranges of heart rate for convenient clinical application, and are believed to be more reliable than those previously suggested.

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142 citations