A Novel Approach in R Peak Detection Using Hybrid Complex Wavelet (Hcw)

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International Journal of Cardiology 124 (2008) 250 – 253 www.elsevier.com/locate/ijcard

Letter to the Editor

A novel approach in R peak detection using Hybrid Complex Wavelet (HCW) P. Jafari Moghadam Fard, M.H. Moradi ⁎, M.R. Tajvidi
Biomedical Faculty, Amirkabir University of Technology, Tehran, Iran Received 1 November 2006; accepted 25 November 2006 Available online 27 March 2007

Abstract In this letter, by design of Complex Morlet Wavelet and Complex Frequency B-Spline Wavelet and linearly combining them, a novel approach, Hybrid Complex Wavelet, has been proposed to identify and detect the components of ECG signal such as QRS complex and R peak. By train and test of implementing the proposed method on both clinically recorded signals from 40 patients and 30 signals of MIT BIH database, we reached better recognition accuracy in comparison to other well-known approaches. © 2007 Elsevier Ireland Ltd. All rights reserved. Keywords: Complex wavelet; Hybrid; Detection; R peak; B-spline

1. Introduction The characteristics of Q, R, S and T, as the ECG signal components, represent the clinical status of a cardiac disease patient, among which the R wave properties have more significant importance. Different Linear, Nonlinear and Morphological algorithms have been proposed to detect QRS complex [1,2]. The morphological algorithms, such as Neural Network, although are slow, but if they are trained well, they could search for and detect a specific characteristic of ECG such as QRS complex [3]. Rapid examples of morphological methods are Wavelet Transform (WT) and Complex Wavelet Transform which do not need to be trained [4–7]. In this letter, Complex Morlet Wavelet (CMW) and Complex Frequency B-Spline Wavelet (CFBSW) are designed and linearly combined together to acquire a more efficient transform named, Hybrid Complex Wavelet

(HCW). This novel wavelet can overcome the deficit of CMW in not detecting all the available R peaks and can overcome the deficit of CFBSW in detecting some redundant R peaks in ECG signal with a satisfactory trade-off between accuracy and rapidity. We have used the cross validation method to train the algorithm and test its performance by some clinically recorded and also some signals from MIT BIH database. Comparing the results of our method with the results of CMW and CFBSW shows better performance in R peak detection. 2. Materials and method 2.1. Wavelet transforms As a morphological method, Continuous Wavelet Transform (CWT) of the signal x(t) is calculated as:   Z 1 t−b CWTða; bÞ ¼ pffiffiffi xðtÞw⁎ :dt ð1Þ a a Where ψ ∈ L2 and ψ⁎ is the complex conjugate of the mother wavelet, a is the dilation level parameter (scale) and b the translation in time.

⁎ Corresponding author. E-mail address: pooria20@gmail.com (M.H. Moradi). 0167-5273/$ - see front matter © 2007 Elsevier Ireland Ltd. All rights reserved. doi:10.1016/j.ijcard.2006.11.236

P. Jafari Moghadam Fard et al. / International Journal of Cardiology 124 (2008) 250–253


This linear combination will be more efficient in detecting all the available R peaks in ECG and consequently, the number of redundant R peaks will be lessened. 2.2. Implementation We have used cross validation method to train and test the algorithm. To acquire a signal with the most correlation to the QRS complex morphological characteristics, a preprocessing band pass frequency filter with cut-off frequencies of 15 and 30 Hz was used to attenuate other unwanted signals and artifacts from every signal. The time-frequency mother wavelet filters, CMW and CFBSW, are designed such that they have the most similarity to the morphological characteristics of QRS complex. While using them in the CWT of ECG signal with a fixed dilation level (scale), they will substitute the QRS complex in ECG signal and after taking the absolute value of CWT decomposition, a waveform similar to the absolute value of the these mother wavelets (Figs. 1c, 2c), could be observed in the...
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