Journal of Medical Engineering

Volume 2015, Article ID 438569, 9 pages

http://dx.doi.org/10.1155/2015/438569

## Identification of Premature Ventricular Cycles of Electrocardiogram Using Discrete Cosine Transform-Teager Energy Operator Model

^{1}Department of ECE, Kamala Institute of Technology & Science, Huzurabad, Telangana 505468, India^{2}Department of ECE, Kakatiya Institute of Technology & Science, Warangal, Telangana 506015, India

Received 31 August 2014; Revised 15 December 2014; Accepted 3 January 2015

Academic Editor: Hasan Al-Nashash

Copyright © 2015 Vallem Sharmila and K. Ashoka Reddy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

An algorithm based on the ability of TEO to track the changes in the envelope of ECG signal is proposed for identifying PVCs in ECG. Teager energy is calculated from DCT coefficients of ECG signal. This method can be considered as computationally efficient algorithm when compared with the well-known DCT cepstrum technique. EPE is derived from the teager energy of DCT coefficients in DCT-TEO method and from the cepstrum of DCT coefficients in the existing method. EPE determines the decay rate of the action potential of ECG beat and provides sufficient information to identify the PVC beats in ECG data. EPEs obtained by DCT-TEO and existing DCT cepstrum models are compared. The proposed algorithm has resulted in performance measures like sensitivity of 98–100%, positive predictivity of 100%, and detection error rate of 0.03%, when tested on MIT-BIH database signals consisting of PVC and normal beats. Result analysis reveals that the DCT-TEO algorithm worked well in clear identification of PVCs from normal beats compared to the existing algorithm, even in the presence of artifacts like baseline wander, PLI, and noise with SNR of up to −5 dB.

#### 1. Introduction

SA node fires electrical impulses at regular intervals that travel through the conduction pathways of cardiac musculature [1]. Only these excitation impulses allow the contraction and expansion of cardiac muscles which when recorded give ECG consisting of three distinct features referred to as P, QRS, and T waves. Depolarization of left and right atria is summed up as P-wave, tall and narrow QRS component reflects the ventricular depolarization, and T-wave is the result of ventricular repolarisation. When SA node fails to function properly, impulses are generated by the atrial or ventricular musculature, which leads to uncoordinated contraction of ventricular muscles in the heart. In response to the impulses generated in the ventricular muscles, ventricular depolarization occurs earlier which is referred to as PVCs. Energy of a normal beat of ECG data is concentrated within a frequency range of 0–17 Hz in frequency domain, whereas energy of an arrhythmia beat of ECG data is spread over longer distance in time domain which reflects that the energy is compressed to a frequency range of 0–4 Hz, so PVCs can be identified using this energy parameter as a measure. Many algorithms were developed in the literature for identification of PVCs [2] based on rhythm analysis and classification of morphological features [3], where R peak detection is required. O’Dwyer et al. [2] proposed that the signal length and its relation to minimum phase correspondent (MPC) can be used to distinguish normal beats from arrhythmia beats. Mandyam et al. [3] showed that QRS width can be chosen as feature vector for arrhythmia classification. DCT was mostly used in image signal processing applications. Kvedalen [4] documented the basic concepts of DCT and its application for image compression. Many linear operators are available for signal analysis but they are not successful for analysis of nonlinear signals like speech and ECG signals. Maragos and Potamianos [5] introduced a nonlinear energy operator TEO, which was found to be successful in the analysis of nonlinear signals. Kamath [6] suggested that TEO, a Teager-Kaiser (1990) operator, is a higher order discrete energy operator when applied to nonlinear signals, yielding energy as a useful parameter. Kaiser [7] studied the basic concepts of TEO and found that TEO can be used for energy extraction from nonlinear signals and achieved successful classification of arrhythmia beats from normal beats. Basic feature of TEO is that it characterizes the energy of the system that generated the signal other than the energy of the signal [8]. Murthy et al. [9] combined the concepts of DCT and homomorphic filtering (cepstrum) for successful identification of PVCs under noisy conditions up to 10 dB. Homomorphic filtering concepts and its application to ECG signal analysis are reported by Murthy and Prasad [10].

DCT is a trigonometric transformation method [4], having a prominent feature of accumulating all the higher energy coefficients of the signal nearer to the origin which motivated us to use DCT. In this paper, a DCT-TEO modeling based algorithm is proposed to extract the energy of ECG beat for identifying PVCs. Many linear energy operators are available in the literature to extract the energy of linear signals that give energy proportional to the square of the amplitude of the signal. Such operators cannot be used for nonlinear signals as their analysis requires amplitude as well as phase or frequency of the signal. A nonlinear energy operator TEO [5–7] is a simple and efficient model developed by Paul et al. [8] to estimate the energy of the source from which the signal is generated using just only three samples. Specialty of TEO lies in its ability to track the changes occurring in the energy of nonlinear components of signals like ECG and it is best suitable for real time signals. Teager energy extracted from DCT coefficients corresponds to the envelope of the system function of ECG. We found the proposed DCT-TEO algorithm as a simple technique that gives remarkable results in distinguishing the PVC beat from normal beat when compared to the well known DCT-cepstrum algorithm [9]. Decay rate of the envelope of ECG beat was used as a measure to identify PVC beats from normal beats of ECG data. Extraction of the envelope or system function requires low-pass filtering of the DCT coefficients of ECG in cepstrum technique whereas the same envelope can be extracted from three samples of DCT coefficients on applying TEO. The remaining work of this paper is arranged in the following way: proposed DCT and its application are explained in Section 2.1, Teager energy operator in Section 2.2, and results and discussion are in Section 3, followed by conclusions in Section 4.

#### 2. Methods

##### 2.1. DCT and Application to ECG

Discrete cosine transform (DCT) can linearly transform the data in time domain to the frequency domain by a set of DCT coefficients [4]. DCT represents the signal or data as a sum of cosine functions with different frequencies. For a given ECG signal for , with equal number of samples around R-peak, point DCT is given as where represent the DCT coefficients or weights and the constant is The ECG signal can be interpreted as the convolution of action potential and excitatory function in time domain equal multiplication of their corresponding DFTs and in frequency domain, expressed by the following equations: Therefore the ECG signal can be decomposed into system and excitatory functions using homomorphic or cepstral filtering [3, 10]. Cepstrum technique involves taking the logarithm of the DFT of a given sequence, which converts the multiplication in frequency domain in addition to cepstral domain. By low-pass filtering the cepstral components, system function can be separated from the excitatory function. The system function shows decaying characteristics due to the decaying nature of the DCT coefficients, which is used as distinguishing feature for PVC detection.

##### 2.2. Teager Energy Operator (TEO)

Energy of a signal is distributed in the frequency band of the signal. One way of defining the energy of a signal is to consider the squared absolute value of the Fourier transform of the given signal. Let be a discrete time signal whose energy is computed as Energy of the signal is given as From the above equations it can be observed that two signals of the same amplitude and different frequencies will exhibit the same energy as the energy is directly proportional to the square of the amplitude of the signal. This is illustrated with an example in Figure 2 by considering a sinusoidal signal of amplitude 2 v and 50 Hz frequency and a second sine wave of amplitude 2 v and 25 Hz with the same sampling frequency is exhibiting the same energy of units. But according to Kaiser, energy required to generate a sine wave varies as a function of both amplitude and frequency from the study of second order differential equation which motivated him to derive Teager energy operator (TEO). TEO concept implies that the energy required to generate a signal is directly proportional to the frequency of the signal. It was observed that the energy required to generate a 50 Hz signal is 7.9 units and energy required to generate a low frequency signal is 1.5 units using TEO from example illustrated in Figure 1.