# Joint reduction of baseline wander, PLI and its harmonics in ECG signal using Ramanujan Periodic Transform

01 Dec 2016-pp 1-5

TL;DR: RPT is used for preprocessing, to reduce baseline wander noise, PLI and its harmonics, and the RPT is reducing the noise with minimum error (E), when compared with notch filter technique.

Abstract: Ramanujan Periodic Transform (RPT) is a newly emerging transformation technique in the field of signal processing. It uses an integer bases (obtained from Ramanujan sum) for transformation. A recorded ECG signal often contains artifacts (bioelectric signals) namely, baseline wander, muscle artifacts (EMG-Electromyogram), motion artifacts, powerline interference (PLI) and its harmonics. With certain precautions during signal recording we can avoid both muscle and motion artifacts. The other noises can be reduced by preprocessing of the recorded ECG signal. In this paper, RPT is used for preprocessing, to reduce baseline wander noise, PLI and its harmonics. The proposed methodology is tested on a record from MIT-BIH Arrhythmia database for different block sizes. A sum (E) of Euclidean errors per block (e i -ith block), is used as a measure to compare the results of RPT with notch filter technique. From the results, the RPT is reducing the noise with minimum error (E), when compared with notch filter technique.

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TL;DR: Using this mixed basis representation, the problem of removing Power Line Interference in ECG data is addressed and the methodology is tested on the MIT-BIH Arrhythmia database and the obtained results are competitive when compared with other techniques.

Abstract: Ramanujan Periodic Transform (RPT) is the newly emerging transform to identify periodicities in the given data RPT represents the given finite length sequence into a weighted linear combination of signals from Ramanujan subspaces RPT has the inability of handling the frequency components with in the Ramanujan subspace This is due to the basis function (Ramanujan sum) used in RPT To overcome this, a new mixed basis representation is proposed which uses both the sequences from Ramanujan subspace and complex exponentials as basis and both the basis are orthogonal to each other Using this mixed basis representation, the problem of removing Power Line Interference (PLI) in ECG data is addressed The methodology is tested on the MIT-BIH Arrhythmia database and the obtained results are competitive when compared with other techniques

5 citations

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TL;DR: This letter introduces a real valued summation known as CCPS and compared CCPT with discrete Fourier transform (DFT) and Ramanujan periodic transform (RPT), it is shown that, using CCPT, it can estimate the period, hidden periods, and frequency information of a signal.

Abstract: This letter introduces a real valued summation known as complex conjugate pair sum (CCPS) . The space spanned by CCPS and its one circular downshift is called complex conjugate subspace (CCS) . For a given positive integer $N\geq 3$ , there exists $\frac{\varphi (N)}{2}$ CCPSs forming $\frac{\varphi (N)}{2}$ CCSs, where $\varphi (N)$ is the Euler's totient function . We prove that these CCSs are mutually orthogonal and their direct sum form a $\varphi (N)$ dimensional subspace $s_N$ of $\mathbb {C}^N$ . We propose that any signal of finite length $N$ is represented as a linear combination of elements from a special basis of $s_d$ , for each divisor $d$ of $N$ . This defines a new transform named as complex conjugate periodic transform (CCPT) . Later, we compared CCPT with discrete Fourier transform (DFT) and Ramanujan periodic transform (RPT). It is shown that, using CCPT, we can estimate the period, hidden periods, and frequency information of a signal. Whereas, RPT does not provide the frequency information. For a complex valued input signal, CCPT offers computational benefit over DFT. A CCPT dictionary based method is proposed to extract non-divisor period information.

4 citations

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TL;DR: It is shown that increasing the number of periods of Ramanujan sums in the filter definition only increases zeros on the unit circle in $z$-plane.

Abstract: Ramanujan filter banks have been used for identifying periodicity structure in streaming data. This letter studies the locations of zeros of Ramanujan filters. All the zeros of Ramanujan filters are shown to lie on or inside the unit circle in the $z$ -plane. A convenient factorization appears as a corollary of this result, which is useful to identify common factors between different Ramanujan filters in a filter bank. For certain families of Ramanujan filters, further structure is identified in the locations of zeros of those filters. It is shown that increasing the number of periods of Ramanujan sums in the filter definition only increases zeros on the unit circle in $z$ -plane. A potential application of these results is that by identifying common factors between Ramanujan filters, one can obtain efficient implementations of Ramanujan filter banks (RFB) as demonstrated here.

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TL;DR: In this paper, an enhanced periodic mode decomposition (EPMD) method is proposed to extract the periodic impulse components from the composite fault signals, and the experimental results indicate that the EPMD is an effective method for composite fault diagnosis of rolling bearings.

Abstract: The impulse components of different periods in the composite fault signal of rolling bearing are extracted difficultly due to the background noise and the coupling of composite faults, which greatly affects the accuracy of composite fault diagnosis. To accurately extract the periodic impulse components from the composite fault signals, we introduce the theory of Ramanujan sum to generate the precise periodic components (PPCs). In order to comprehensively extract major periods in composite fault signals, the SOSO-maximum autocorrelation impulse harmonic to noise deconvolution (SOSO-MAIHND) method is proposed to reduce noise and enhance the relatively weak periodic impulses. Based on this, an enhanced periodic mode decomposition (EPMD) method is proposed. The experimental results indicate that the EPMD is an effective method for composite fault diagnosis of rolling bearings.

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TL;DR: In this paper, a real valued summation known as complex conjugate pair sum (CCPS) is introduced, where the space spanned by CCPS and its one circular downshift is called the complex conjugate subspace (CCS).

Abstract: This letter introduces a real valued summation known as Complex Conjugate Pair Sum (CCPS). The space spanned by CCPS and its one circular downshift is called {\em Complex Conjugate Subspace (CCS)}. For a given positive integer $N\geq3$, there exists $\frac{\varphi(N)}{2}$ CCPSs forming $\frac{\varphi(N)}{2}$ CCSs, where $\varphi(N)$ is the Euler's totient function. We prove that these CCSs are mutually orthogonal and their direct sum form a $\varphi(N)$ dimensional subspace $s_N$ of $\mathbb{C}^N$. We propose that any signal of finite length $N$ is represented as a linear combination of elements from a special basis of $s_d$, for each divisor $d$ of $N$. This defines a new transform named as Complex Conjugate Periodic Transform (CCPT). Later, we compared CCPT with DFT (Discrete Fourier Transform) and RPT (Ramanujan Periodic Transform). It is shown that, using CCPT we can estimate the period, hidden periods and frequency information of a signal. Whereas, RPT does not provide the frequency information. For a complex valued input signal, CCPT offers computational benefit over DFT. A CCPT dictionary based method is proposed to extract non-divisor period information.

##### References

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TL;DR: A real-time algorithm that reliably recognizes QRS complexes based upon digital analyses of slope, amplitude, and width of ECG signals and automatically adjusts thresholds and parameters periodically to adapt to such ECG changes as QRS morphology and heart rate.

Abstract: We have developed a real-time algorithm for detection of the QRS complexes of ECG signals. It reliably recognizes QRS complexes based upon digital analyses of slope, amplitude, and width. A special digital bandpass filter reduces false detections caused by the various types of interference present in ECG signals. This filtering permits use of low thresholds, thereby increasing detection sensitivity. The algorithm automatically adjusts thresholds and parameters periodically to adapt to such ECG changes as QRS morphology and heart rate. For the standard 24 h MIT/BIH arrhythmia database, this algorithm correctly detects 99.3 percent of the QRS complexes.

5,782 citations

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TL;DR: A method for the automatic processing of the electrocardiogram (ECG) for the classification of heartbeats and results are an improvement on previously reported results for automated heartbeat classification systems.

Abstract: A method for the automatic processing of the electrocardiogram (ECG) for the classification of heartbeats is presented. The method allocates manually detected heartbeats to one of the five beat classes recommended by ANSI/AAMI EC57:1998 standard, i.e., normal beat, ventricular ectopic beat (VEB), supraventricular ectopic beat (SVEB), fusion of a normal and a VEB, or unknown beat type. Data was obtained from the 44 nonpacemaker recordings of the MIT-BIH arrhythmia database. The data was split into two datasets with each dataset containing approximately 50 000 beats from 22 recordings. The first dataset was used to select a classifier configuration from candidate configurations. Twelve configurations processing feature sets derived from two ECG leads were compared. Feature sets were based on ECG morphology, heartbeat intervals, and RR-intervals. All configurations adopted a statistical classifier model utilizing supervised learning. The second dataset was used to provide an independent performance assessment of the selected configuration. This assessment resulted in a sensitivity of 75.9%, a positive predictivity of 38.5%, and a false positive rate of 4.7% for the SVEB class. For the VEB class, the sensitivity was 77.7%, the positive predictivity was 81.9%, and the false positive rate was 1.2%. These results are an improvement on previously reported results for automated heartbeat classification systems.

1,232 citations

### "Joint reduction of baseline wander,..." refers background in this paper

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TL;DR: What PhysioNet offers to researchers is discussed, some of the technology needed to support these functions are described, and observations gleaned from the organisation's first year of service are concluded.

Abstract: Free access to a signals archive and a signal processing/analysis software library fosters online collaboration. This article aims to introduce PhysioNet as a resource to the biomedical research community. After a capsule summary of its history and goals, we discuss what PhysioNet offers to researchers, describe some of the technology needed to support these functions, and conclude with observations gleaned from PhysioNet's first year of service.

300 citations

### "Joint reduction of baseline wander,..." refers background in this paper

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TL;DR: In the companion paper (Part II), it is shown that arbitrary finite duration signals can be decomposed into a finite sum of orthogonal projections onto Ramanujan subspaces.

Abstract: The famous mathematician S. Ramanujan introduced a summation in 1918, now known as the Ramanujan sum c_q(n). For any fixed integer q, this is a sequence in n with periodicity q. Ramanujan showed that many standard arithmetic functions in the theory of numbers, such as Euler's totient function φ(n) and the Mobius function μ(n), can be expressed as linear combinations of c_q(n), 1 ≤ q ≤ ∞. In the last ten years, Ramanujan sums have aroused some interest in signal processing. There is evidence that these sums can be used to extract periodic components in discrete-time signals. The purpose of this paper and the companion paper (Part II) is to develop this theory in detail. After a brief review of the properties of Ramanujan sums, the paper introduces a subspace called the Ramanujan subspace S_q and studies its properties in detail. For fixed q, the subspace S_q includes an entire family of signals with properties similar to c_q(n). These subspaces have a simple integer basis defined in terms of the Ramanujan sum c_q(n) and its circular shifts. The projection of arbitrary signals onto these subspaces can be calculated using only integer operations. Linear combinations of signals belonging to two or more such subspaces follows certain specific periodicity patterns, which makes it easy to identify periods. In the companion paper (Part II), it is shown that arbitrary finite duration signals can be decomposed into a finite sum of orthogonal projections onto Ramanujan subspaces.

99 citations

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TL;DR: This paper presents an individual identification system using single lead electrocardiogram (ECG) designed on template matching and adaptive thresholding, and shows the performance of P and T wave delineators is optimum and also stable in comparison to other published results.

Abstract: This paper presents an individual identification system using single lead electrocardiogram (ECG). The proposed techniques for P and T wave delineation are based on time derivative and adaptive thresholding. The performance of proposed delineators is evaluated on manually annotated Physionet QT database. The accuracy of delineators are quantified on mean error and standard deviation of differences between manually annotations and automated results. Especially, lower values of error in standard deviation for onset and offset of P wave fiducials are obtained as 8.1 and 6.29 while for T wave fiducials are 9.4 and 11.2 (where units are in ms). It shows the performance of P and T wave delineators is optimum and also stable in comparison to other published results. Found fiducials are processed for the extraction of heartbeat features. From each heartbeat, 19 stable features related to interval, amplitude and angle are computed. The feasibility of ECG as a new biometric is tested on proposed identification system designed on template matching and adaptive thresholding. The accuracy of identification system is achieved to 99% on the datasize of 125 recordings prepared from 25 individual ECG of Physionet.

98 citations

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