Efficient reduction of PLI in ECG signal using new variable step size least mean fourth adaptive algorithm

Received Des 27, 2017 Revised Oct 8, 2018 Accepted Oct 30, 2018 It is very important in remote cardiac diagnosis to extract pure ECG signal from the contaminated recordings of the signal. When recording the ECG signal in the laboratory, the signal is affected by numerous artifacts. Varies artifacts generally degrades the signal quality are PLI, EM, MA and EM. In addition to these, the channel noise also added when transmitting signal from remote location to diagnosis center for analyzing the signal. There are several approaches are used to reduce the noise present in the ECG signal. From the literature it is proven that compared to non adaptive filters, adaptive filters play vital role to trace the random changes in the corrupted signals. In this paper, we proposed efficient Variable step size leaky least mean fourth algorithm and its sign versions for reducing the complexity. These algorithms shows that it gives low steady state error due to least mean fourth and fast convergence rate that is it tracks the input signal quickly because of its variable step size is high at initial iterations of signal compared to the LMS algorithm. The performance of the algorithm is evaluated using SNR, frequency spectrum, MSE, misadjustment and convergence characteristics.


INTRODUCTION
ECG is one of the most direct ways to study the cardiac condition. Any cardiac abnormalities will be clearly seen through investigation of the ECG signals. This provides doctors with the most updated cardiac condition of the patient so that proper treatment can be given [1]. Biotelemetry is a technology where wireless communication is utilized in health care applications to transmit biological or physiological data to a distant place then ECG specialist has the capability to interpret the data and affect decision-making [2]. Telecardiology is a special branch of biotelemetry in which the ECG signals are processed wirelessly between the patient and diagnostic centre. While transmitting the ECG signal from patient end to diagnostic centre, several artifacts may add to ECG signal. These artifacts strongly affect/degrade the signal quality of ECG signals and masks tiny features [3,4].
To improve the signal quality in terms of signal to noise ratio and to reduce noises present in the signal then different filtering techniques are used. In the literature there are several filtering techniques are used to remove the artifacts present in ECG signal [5][6][7]. Butt et al. [7], presented the PLI noise reduction in the ECG signal using SSRLS filter, in this, result analysis it gives the superior performance as compared with the notch filter of varying attenuation levels. Hamilton [8] compared the performance of adaptive and nonadaptive notch filters used to remove the single-frequency component present in PLI. Kadam et al. [9] described a PLI subtraction technique. In referred paper, different digital FIR windowing techniques are used Shin et al. [10] proposed a variable step size affine projection algorithm and a variable step size normalized LMS algorithm methods. In this simulation results analysis they proved that these algorithms to get faster convergence rate and less misadjustment value. Similarly, Vega et al. [11] presented a robust VSSNLMS algorithm for system identification and removal of echo's based on norm of the filter update. But complexity of this algorithm is large. Another VSSNLMS was developed for cancellation of residual echo's produced by the part of the systems by Paleologu et al. [12].
In this paper, we proposed a new Variable Step Size Least Mean Fourth (VSS-LMF) algorithm which gives less computational complexity and low misadjustment value. For further reducing computational complexity we applied signum function to this algorithm and derived three other algorithms. These four algorithms gives better signal to noise ratio compared to LMS algorithm and VSSLMS algorithm in terms of removal of artifacts present in the ECG signal. From the simulation results it is verified that VSS-Sign Regressor LMF algorithm gets better reduction of noise present in ECG signal compared to other derived algorithms and LMS algorithm.

ADAPTIVE ALGORITHM
The adaptive LMS algorithm was invented by Widrow and Hoff in 1959 [13,14]. The LMS algorithm can be considered as the simplest form of steepest decent algorithm. The LMS algorithm is composed by two basic processes, Filtering process and an adaptive process. The structure of adaptive filter is shown in the  The parameter  describes the rate at which convergence of the algorithm starts and finally reaches to Wiener optimum solution. The problem with LMS algorithm [13] is that selecting the step size parameter  smaller then convergence will be slow but the steady state error will be small and vice versa. So selecting the proper value of  is difficult in the LMS algorithm. Therefore the variable step-size gives a trade-off between steady state misadjustment and convergence rate of the algorithm. This problem motivates to use the step size as variable, rather than fixed [15,16]. Adaptive filters based on higher order (like fourth order)

Int J Elec & Comp Eng
ISSN: 2088-8708  Efficient reduction of PLI in ECG signal using new variable step size least mean fourth… (T. Gowri) 309 statistics gives better performance (less error) than the mean square like LMF [17] performs better than the mean square utilized in the LMS algorithm in particular situations. The small modification in (1), leads weight update equation for VSS-LMF algorithm which is defined as (2): j is a scalar variable step-size parameter and is considered as (3): where 'j' is the occurrence number in the iteration. (3) leads the fast convergence rate at the beginning of the signal occurrences due to a large variable step size, and decreasing the step size in the latter cases to a less misadjustment error ratio, and then finally it reaches to a steady state value. ' ' is constant parameter, in this analysis the values chosen is 0.9 which gives better result. This decreasing step size is the main variation in the VSS-LMF which is not possible in LMS. The VSS-LMF algorithm (2) requires L+3 multiplication. These "multiply and accumulate" (MAC) operations are reduced by adding signum function to the (2). These reduced complexity algorithms are very useful to design digital signal processing devices and field programmable gate arrays. The complexity of the algorithm further reduced by using the signum function and it is defined as (4): The signum (polarity) function can be applied to the data in the weight update (2), then new derived algorithm is VSS-Sign Regressor LMF algorithm and is given by (5): The number of multiplications required for VSS-SRLMF algorithm is 3, so compared to VSS-LMF algorithm 'L' number of multiplications reduced. So the complexity of the circuit is reduced for designing process. By applying signum function to the error function in the VSS-LMF algorithm, the new algorithm is named as VSS-Sign LMF algorithm and its weight update equation is as (6): The number of multiplications required for VSS-SLMF algorithm is L+1. The signum can also be applied for both error and data functions in (2), the new algorithm is known as VSS-Sign Sign LMF algorithm is given by (7): The VSS-SSLMF algorithm requires only one multiplication, compared to all above algorithms this algorithm requires less complexity. So finally in this paper totally four algorithms developed, whose performance characteristics are analyzed by reducing artifact in the ECG signal.

SIMULATION RESULT AND ANALYSIS
The ability of varies derived algorithms are tested by taking real ECG signal from the MIT-BIH arthymia database [18] by adding different artifacts. In this data base there are totally 48 ECG records are digitized with a sampling frequency of 360 Hertz per channel. From the 48 ECG data records, 22 data's are from women and 25 data's are from men with different age groups are collected. From the ECG data records 201 and 202 data records are collected from the single person. The ECG signal is corrupted with a power line  From the Figure 3(a) it shows that pure ECG signal is corrupted with PLI and Figure 3(b-e) shows that removal of PLI noise using different derived adaptive algorithms. From the figure we can see that at starting iterations there is small residue noise present, when number of iterations increases then noise elimination is more that is minimum steady state error we can get due to variable step size. It is observed that VSS-LMF and VSS-SRLMF algorithms reduce PLI noise as high compared to other two algorithms. The performance of the removal of PLI using various algorithms is measured in terms of SNR, as shown in Table 1 The convergence curves for different adaptive algorithms in terms number of iterations verses mean square error as shown in Figure 4. These characteristics are drawn for ECG record number 103. From the convergence characteristics it is observed that VSS-SRLMF algorithm gives fast convergence rate as compared to other adaptive algorithms and VSS-SLMF algorithm gets slow convergence rate.  Table 2. From the Table 2, VSS-LMF algorithm gets 2.87e-04 MSE, which is low compared to other algorithms, then after VSS-SRLMF algorithm gets 3.43e-04 MSE which is also low compared to LMS and other sign based algorithms. The ratio of excess MSE to minimum MSE gives Misadjustment. Step Size-LMF based adaptive algorithms are developed. The variable of step size for each iteration leads to fast convergence. To achieve fast data transmission rate it is desirable to reduce the computational complexity. This can be done by signed algorithms which are derived from conventional algorithm. The three versions of signed algorithms are derived. So totally four adaptive noise cancellers are developed and tested on ECG signals for cancellation of PLI noise. Among these sign regressor VSS-LMF algorithms performs better SNR with less computational complexity as well as fast convergence as that of VSS-LMF algorithm. These derived algorithms can also be applied for other artifacts which will give better elimination of noise.