Introduction
Cardiovascular diseases are among the leading causes of death in the world. According to the World Health Organization (WHO), about 30% of these causes of death worldwide are related to cardiovascular problems. These numbers are closely linked to people’s lifestyle and been increasing every year, generating greater concern on many health organizations (^{World..., 2017}). More effective health actions are required, like prevention programs, diagnosis and treatment. In this sense, several technologies and methods have been developed to improve the health service in order to reduce the number of deaths and the costs involved with the healthcare system interventions ( ^{Braunwald et al., 2002} ; ^{Valentim et al., 2015} ).
Currently, an alternative that have been improved in the primary healthcare system is the telecardiology, which enables patients telemonitoring, ensuring continuous vital signs monitoring, and provide greater mobility and comfort for patients ( ^{Chong et al., 2015} ; ^{Gagnon et al., 2006} ; ^{Hersh et al., 2001} ; ^{Valentim et al., 2015} ). In this way, the automatic detection of cardiac signals (electrocardiogram - ECG) is important to cardiac disease diagnosis, and can be used like medical diagnosis assistance tool. However, the automatic ECG analyzing systems performance depends heavily upon the reliable and accurate detection of the ECG signal characteristic (QRS complex, as well as the P and T waves) ( ^{Dalvi et al., 2016} ; ^{Gadêlha et al., 2012} ; ^{Martis et al., 2014} ; ^{Valentim et al., 2015} ).
In this work, an algorithm based on ECG signal with real-time approach has been developed in order to detect heart disease, in particular the Premature Ventricular Contraction (PVC) occurrence. The ECG reflects the heart electrical activity, it is a recording of the electric potential generated by electric behavior of the cardiac muscle tissue, the heart, and provides information about the heart state, enabling several noninvasive diagnostic of heart disease ( ^{Clifford et al., 2006} ; ^{Malmivuo and Plonsey, 1995} ; ^{Zago et al., 2015} ). Thus, a system that analyzes PVC is proposed, that is among the most common types of ventricular cardiac arrhythmia ( ^{Mann et al., 2014} ; ^{Morris et al., 2009} ; ^{Natale, 2007} ).
The PVC is a cardiac rhythm abnormalities resulted from ectopic foci in the ventricles, and it is independent of the sinoatrial node pace set. It is frequently originated from the right ventricular outflow tract, but some can be originated from the left ventricular outflow tract, from aortic sinus cusp, from tricuspid and mitral valve annulus, and from coronary venous system, among other heart structures ( ^{Ge et al., 2012} ; ^{Jia et al., 2011} ; ^{Sayadi et al., 2010} ; ^{Zheng et al., 2016} ).
The PVC generates one heartbeat that occurs abnormally early of the normal sinus rhythm, and usually it is not associated with P wave. This electrical event usually causes a break in the normal sinus heart activity — this break results from the gap between the PVC and the next normal heartbeat and is called compensatory pause ( ^{Malmivuo and Plonsey, 1995} ; ^{Mann et al., 2014} ; ^{Natale, 2007} ).
The PVC can occurs in person of any age and not necessarily represent cardiac risk, however it only pose danger if the person has any heart disease, such as heart failure. Thus, this is an important factor to consider in heart disease people. Recent studies indicate that the PVC can be an indicative of sudden cardiac death risk, and it is associated with mortality from acute myocardial infarction ( ^{Hirose et al., 2010} ; ^{Inan et al., 2006} ; ^{Iwasa et al., 2005} ; ^{Lek-uthai et al., 2014} ). Therefore, the PVC detection has a particular interest for patients with heart disease treatment.
Hence, in the last years, several PVC detection system have been proposed for this issue: based on Artificial Neural Network (ANN) ( ^{Bortolan et al., 1991} ; ^{Dalvi et al., 2016} ; ^{Hu et al., 1997} ; ^{Inan et al., 2006} ), Heuristic algorithm ( ^{Dotsinsky and Stoyanov, 2004} ), Bayesian framework ( ^{Sayadi et al., 2010} ), Support Vector Machine (SVM) ( ^{Shen et al., 2011} ), morphology ECG features ( ^{Chazal and Reilly, 2006} ; ^{Chazal et al., 2004} ; ^{Lek-uthai et al., 2014} ), Fuzzy Neural Network System (FNNS) ( ^{Lim, 2009} ), Wavelet Transform ( ^{Inan et al., 2006} ; ^{Martis et al., 2013} ; ^{Nazarahari et al., 2015} ; ^{Orozco-Duque et al., 2013} ; ^{Shyu et al., 2004} ; ^{Yochum et al., 2016} ) and adaptive filter ( ^{Nieminaki et al., 1999} ; ^{Solosenko et al., 2015} ). The main feature of most detection methods is a real-time analysis, however some methods have high mathematical complexity, which demands a high computational cost.
This paper presents a Wavelet-based algorithm for PVC detection, with a real-time approach. Adaptive threshold methods were used in parallel with the Wavelet Transform and the system was validated on MIT-BIH Arrhythmia Database ( ^{Moody and Mark, 2001} ; ^{Goldberger et al., 2000} ). It was implemented the Redundant Discrete Wavelet Transform (RDWT), aiming a lower computational complexity.
Methods
Wavelet transform
The Wavelet Transform (WT) has been widely used in recent years in various areas and several applications, such as power system quality ( ^{Andrade and Leao, 2014} ; ^{Arrais et al., 2014} ; ^{Costa, 2014} ), signal processing ( ^{Pedireddi and Srinivasan, 2010} ; ^{Saleh et al., 2012} ), biomedical engineering ( ^{Arrais et al., 2016} ; ^{Dalvi et al., 2016} ; ^{Di Marco and Chiari, 2011} ; ^{Kim et al., 2011} ; ^{Madeiro et al., 2009} ), among others. WT provides a compact and flexible analysis in time and frequency domain, allowing different resolution levels, besides presenting various base functions (Wavelet families), which allow a more specific analysis in order to adapt the analysis of signal behavior and so achieve the best possible results ( ^{Burrus et al., 1997} ; Mallat, ^{1989} , ^{2008} ; ^{Percival and Walden, 2000} ).
WT allows multiresolution analysis, such that a discrete signal can be decomposed and analyzed at different resolution levels (or scales) ( ^{Burrus et al., 1997} ; Mallat, ^{1989} , ^{2008} ). Thus, a discretized signal can be decomposed in terms of wavelet coefficients and scaling coefficients at various levels of resolution through a digital filtering process. This filtering process divides the input signal into two frequency bands, high frequency signals and low frequency signals. The wavelet coefficients is the high-pass filters results and the scaling coefficients is the low-pass filters results ( ^{Burrus et al., 1997} ; Mallat, ^{1989} , ^{2008} ; ^{Percival and Walden, 2000} ).
Wavelet Transforms can be used for continuous time (Continuous Wavelet Transform - CWT) or discrete time (Discrete Wavelet Transform - DWT) signals applications. In relation to basic functions there are several Wavelet families as Morlet, Biorthogonal, Mexican Hat, Harr, Daubechies, Meyer, Coiflets, Symlets, and many others, both in the Real domain and Complex domain numbers ( ^{Daubechies, 1992} ; ^{Grossmann and Morlet, 1984} ; ^{Mallat, 2008} ; ^{Percival and Walden, 2000} ).
For cardiac signal analysis the Wavelet family most used is the Daubechies, especially the mother Wavelet db4 ( ^{Arrais et al., 2016} ; ^{Sasikala and Wahidabanu, 2010} ; ^{Singh and Tiwari, 2006} ). However, the ECG signal analysis with db4 explanation is not clear in this works. In this paper is used the Redundant Discrete Wavelet Transform (RDWT), a DWT variant version, and is compared the system performance with some mother wavelets from Daubechies, Coiflets and Symlets Wavelet families in order to find the best mother wavelet for ECG signals analysis application.
Redundant discrete wavelet transform
RDWT is a DWT variant version, and presents the basic characteristics of it: the original signal is decomposed into two components, wavelet and scaling coefficients, and the filter coefficients for the calculation of each component are related, the high-pass and low-pass filters, respectively ( ^{Daubechies, 1992} ; ^{Grossmann and Morlet, 1984} ; ^{Mallat, 2008} ; ^{Percival and Walden, 2000} ). Although the DWT provides relatively simple implementation complexity, speed and low computational effort, the RDWT has become interesting due to the fact that DWT present some limitations for some specific applications such as the detection of the QRS complex in real-time analysis ( ^{Arrais et al., 2016} ).
The major difference between the DWT and RDWT is the subsampling process: the DWT presents time variant behavior due to the subsampling process used to calculate the wavelet and scaling coefficients, whereas the RDWT not present the subsampling process, so this mathematical tool provides time invariant behavior, resulting in less significant delay over the signal reconstruction process if compared to DWT ( ^{Arrais et al., 2016} ; ^{Percival and Walden, 2000} ). In general, the main differences are listed below:
RDWT can be applied to any number of samples, whereas DWT requires is a power of two number sample due to the subsampling process by two;
DWT is an orthonormal transformation, whereas RDWT is a non orthogonal transformation;
RDWT is an invariant time transform, since it does not perform subsampling process by two in the signal sample, whereas DWT performs the subsampling process by two, resulting in a time variant behavior.
The RDWT mathematical model for real-time approach is given by the following equations ( ^{Arrais et al., 2014} ; ^{Costa and Driesen, 2013} ): The Equation 1 provides the scaling coefficients, s_{j}, and the Equation 2 provides the wavelet coefficients, ω_{j}, both in the level resolution (scale) j, obtained by convolution of the scaling coefficients s_{j-1} by
since
Figure 1 shows a decomposition process block diagram for RDWT of a signal x_{0} (s_{0}) with sampling frequency (f_{s} ) in two resolution level (first and second scale), that provides the scaling (s _{1} and s_{2}) and wavelet (ω _{1} and ω_{2}) coefficients. This decomposition process is based on the pyramidal algorithm of Mallat ( ^{Mallat, 1989} , ^{2008} ). The filters coefficients
The signal energy can be calculated based on the scaling and wavelet coefficients: in according to Parseval’s theorem, the signal energy can be partitioned in terms of the wavelet and scaling coefficients energy ( ^{Burrus et al., 1997} ). In other words, the energy of the original signal x_{0}, with k_{t} sample, is equal to the sum of the wavelet coefficients energies of all resolution levels, 1 ≤ j ≤ J, with the scaling coefficients energy of the last resolution level, J, with J ≤ J_{max} ( ^{Burrus et al., 1997} ; ^{Costa and Driesen, 2013} ). The energy signal can be calculated by Equation 5:
where:
Benchmark databases
Several standard ECG databases are available for the evaluation of heart disease detection algorithms ( ^{Kohler et al., 2002} ; ^{Martis et al., 2014} ). The algorithm performance on a standard database is not the main parameter to propose to apply in a clinical environment, but it provides a good performance comparison between algorithm detections. In this research work was used the MIT/BIH arrhythmia database, since it is one of the most used to evaluate the algorithm ECG detections ( ^{Arrais et al., 2016} ; ^{Hamilton and Tompkins, 1986} ; ^{Li et al., 1995} ; ^{Martinez et al., 2004} ; ^{Pan and Tompkins, 1985} ).
This database is obtained over 4,000 long-term Holter recordings at Beth Israel Hospital Arrhythmia Laboratory between the years of 1975 and 1979 from patients under different cardiac arrhythmias. It contains 48.5 hours of recordings with two-channel and sampling rate of 360 Hz. However, only one of the ECG channels was used (channel 1 - a modified limb lead II (MLII)). However, the database contains records of modified leads V1, V2 and V5, and, in one instance, also V4. The subject’s records were obtained from 25 men aged 32 to 89 years, and 22 women aged 23 to 89 years ( ^{Goldberger et al., 2000} ; ^{Moody and Mark, 2001} ). It was analyzed 36 recordings, although the database contains 48 recordings, by reason of external noise in some recordings that disturbed the ECG signal behavior.
System description
The system for PVC detection is based on the RDWT and adaptive threshold methods. It was described on Matlab 2014a platform version. The Figure 2 shows the system description flowchart. The RDWT provides two coefficients, the scaling and the wavelet coefficients, and the algorithm proposed is based on the energy wavelet coefficients for PVC detection. The ECG features is obtained with the RDWT and the detection process is through adaptive threshold methods based on mean value ECG signal energy on all resolution levels, therefore there is one threshold for each level.
In the proposed system, each ECG signal sample (data record from MIT-BIH databases) is analyzed in real-time approach. The RDWT-based energy wavelet coefficients are analyzed to detect the PVC. Each energy wavelet coefficient sample is compared with a threshold value, and if it is higher than the threshold value, the sample is a possible PVC occurrence indicative. Hence, this sample is stored and will be compared with the next sample (remaining). Therefore, these selected samples are compared and the one that has the highest value (amplitude peak) corresponds to the energy maximum value and a PVC occurrence.
The energy PVC value is much higher than the normal ECG energy module value. For this reason that the PVC can be detect based on energy signal. The variable e[n] is the n sample energy wavelet coefficients, provided by RDWT. It is used an auxiliary variable E_{p_aux} to store a temporary energy sample value. The threshold value thr is obtained from empirical way, according to computed test, and it is used to detect the possible PVC occurrence. The threshold value is updated in according to the mean energy value in each minute ECG record.
If the energy wavelet coefficient sample (e[n]) is greater than the threshold (thr), this sample is stored in the auxiliary variable E _{aux}. Then, the algorithm compares each value E_{aux} with the next sample. Then, the current sample is stored in E_{aux} and the last sample in the E_{p_aux}. When the current sample (Eaux) is less than the previous sample (Epaux), this sample is stored in a vector E_{P}[n], and this indicates possible PVC. Thus, the ECG signal is analyzed and all indicative PVC occurrences are stored in a vector.
In this work the RDWT was implemented with six resolution levels (or scale). The sample frequency used was 350 Hz, in order to optimize the distribution of the ECG signal energy into resolution levels, to facilitate the signal analysis, according to ECG power spectra ( ^{Thakor et al., 1984} ). The Table 1 presents the frequency bands for each RDWT resolution level of the wavelet coefficients.
Results
In this paper it was analyzed the effect of the wavelet families Daubechies, Coiflets and Symlets, in order to find the best wavelet for ECG proposed analysis. This analyze motivation by virtue of many works use the mother wavelet db4 (Daubechies family), but the reason is not clear. The Table 2 shows the comparative results, based on standard deviation analysis between the ECG energy signal and the energy scaling coefficients at all resolution level. It was analyzed the following mother wavelets: Daubechies (db2, db4, db6, db8, and db12), Coiflets (coif6, coif12 and coif18) and Symlets (sym4, sym6, sym8 and sym10).
Scale | Daubechies | Coiflets | Symlets | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
db2 | db4 | db6 | db8 | db12 | coif6 | coif12 | coif18 | sym4 | sym6 | sym8 | sym10 | |
1 | 0.911 | 0.972 | 0.990 | 0.997 | 0.998 | 0.998 | 0.973 | 0.997 | 0.992 | 0.972 | 0.990 | 0.997 |
2 | 1.000 | 0.410 | 0.298 | 0.271 | 0.269 | 0.279 | 0.424 | 0.354 | 0.470 | 0.410 | 0.298 | 0.269 |
3 | 1.000 | 0.729 | 0.651 | 0.615 | 0.594 | 0.581 | 0.721 | 0.571 | 0.547 | 0.729 | 0.651 | 0.616 |
4 | 1.000 | 0.926 | 0.904 | 0.894 | 0.888 | 0.883 | 0.923 | 0.881 | 0.872 | 0.926 | 0.904 | 0.894 |
5 | 1.000 | 0.900 | 0.875 | 0.865 | 0.860 | 0.857 | 0.897 | 0.854 | 0.847 | 0.900 | 0.875 | 0.865 |
6 | 0.905 | 0.970 | 0.989 | 0.997 | 0.999 | 0.998 | 0.972 | 0.997 | 0.992 | 0.970 | 0.989 | 0.997 |
The energy coefficients standard deviation provides a good dispersion measure to verify the energy behavior ECG signal analyzed by the pyramidal algorithm, since the energy loss in the detection process will result in low performance. This analysis was computed for all resolution level in order to find the lowest variation of the standard deviation between the levels.
Based on the results the lowest mother wavelet filter order provides the best standard deviation between the energy original signal and the wavelet coefficients energy for each level. So, the reliability and effectiveness of cardiac signal analysis algorithms based on Wavelet Transform are closely linked to the wavelet filters order used, with better results for low-order filters. Thereby, due to this comparative study, it was chosen the Daubechies Wavelet family for signal analysis.
Although the study indicates that db2 is the best for ECG application, in this paper the mother Wavelets db2, db4, coif6 and sym4 were verified, in order to ascertain which provides the best performance, since these mother wavelets provided the lowest standard deviation value for their respective wavelet families. This motivation is also due to the large amount of works that use db4 for ECG analysis and the search for a faster algorithm.
The system was validated on MIT-BIH Arrhythmia Database ( ^{Goldberger et al., 2000} ; ^{Moody and Mark, 2001} ), and the detection algorithms performance is evaluated according to three parameters, Sensitivity (Se), Positive Predictivity (P+) and Specificity (Sp) ( ^{Kohler et al., 2002} ; ^{Wang, 2013} ):
where TP is the True Positive, the FN is the False Negative, FP the False Positive and TN the True Negative values.
Figure 3 shows the algorithmic results based on db2 mother wavelet for the record 100 analysis from MIT-BIH Arrhythmia Database. Figure 3 a is a range time where occurs a PVC. Figure 3 b presents the wavelet coefficients for this range time. It can be observed that larger variations are observed on the scales 3 (ω_{3}) and 4 (ω _{4}), but during the PVC a larger variations are observed on the scales 4 (ω_{4}), 5 (ω_{5} ) and 6 (ω_{6}), principally the coefficients in the scale 5 (ω_{5}). It can be verified that when a PVC occurs the wavelet coefficients increase, if compared to normal heartbeat wavelet coefficients.
The largest variation observed on wavelet coefficients at scale 5 (ω _{5}) implies that the highest energy portion is on the scale 5. Figure 3 c illustrates the wavelet coefficients energy on the six resolutions levels. It can be verified that the energy increases enough when the PVC occurs, and this event can indicate a PVC occurrence. The energies values increase in all resolution levels, but in last three levels are most significant, in specially at level 5 (wavelet coefficients energy ω_{5} ), and associated with threshold methods can detect the PVC occurrence.
Figure 4 shows the algorithm results based on db2 mother wavelet for the record 102 analysis (MIT-BIH Arrhythmia Database). In this case, there is a change in the ECG signal behavior after the occurrence of the PVC due to the action of a pacemaker ( Figure 4 a), to control the heart rate. Figure 4 b presents the wavelet coefficients energy on all scales (ω1, ω2, ω3, ω4, ω5 and ω6). If compared to Figure 3 , the highest energy portion is concentrated in the 6^{th} scale, but the energies are also most significant on last two scale. So the detection can occur in any scale or more than one, and the threshold technical provides good comparative analysis for all resolution level.
Table 3 presents the algorithm comparative results on the following mother wavelets: db2, db4, coif6 and sym4. The table shows the Sensitivity (Se), Positive Predictivity (P+) and Specificity (Sp) parameters used for PVC detection performance comparison.
Mother Wavelet | Se (%) | P^{+} (%) | Sp (%) |
---|---|---|---|
db2 | 99.18 | 99.15 | 99.94 |
db4 | 99.23 | 99.09 | 99.96 |
coif6 | 97.12 | 96.20 | 99.70 |
sym4 | 99.23 | 99.09 | 99.96 |
Table 4 presents the system analysis based on db2 for 36 records from MIT-BIH Arrhythmia Database, on 80.872 annotated beats, being 3.408 annotated PVC beats. The table shows besides the PVC detected for each data record, the True Positive (TP) and True Negative (TN) value, the False Positive (FP) and False Negative (FN) value, and amount of failures.
Data record | Total beats |
Total PVC |
TP | TN | FP | FN | Failed detection | Failed detection (%) |
---|---|---|---|---|---|---|---|---|
100 | 2273 | 1 | 1 | 2272 | 0 | 0 | 0 | 0 |
101 | 1865 | 1 | 1 | 1864 | 0 | 0 | 0 | 0 |
102 | 2187 | 4 | 4 | 2183 | 0 | 0 | 0 | 0 |
103 | 2084 | 0 | 0 | 2084 | 0 | 0 | 0 | 0 |
105 | 2572 | 41 | 36 | 2526 | 0 | 5 | 5 | 12.20 |
106 | 2027 | 520 | 520 | 1507 | 0 | 0 | 0 | 0 |
107 | 2137 | 59 | 69 | 2068 | 8 | 2 | 10 | 16.95 |
108 | 1763 | 17 | 17 | 1746 | 0 | 0 | 0 | 0 |
109 | 2532 | 38 | 38 | 2494 | 0 | 0 | 0 | 0 |
111 | 2124 | 1 | 1 | 2123 | 0 | 0 | 0 | 0 |
112 | 2539 | 0 | 0 | 2539 | 0 | 0 | 0 | 0 |
113 | 1795 | 0 | 0 | 1795 | 0 | 0 | 0 | 0 |
114 | 1879 | 43 | 47 | 1832 | 4 | 0 | 4 | 9.30 |
115 | 1953 | 0 | 0 | 1953 | 0 | 0 | 0 | 0 |
116 | 2412 | 109 | 99 | 2293 | 1 | 9 | 10 | 9.17 |
117 | 1535 | 0 | 0 | 1535 | 0 | 0 | 0 | 0 |
119 | 1987 | 444 | 424 | 1523 | 4 | 16 | 20 | 4.50 |
121 | 1863 | 1 | 0 | 1861 | 0 | 1 | 1 | 100 |
122 | 2476 | 0 | 0 | 2476 | 0 | 0 | 0 | 0 |
123 | 1518 | 3 | 3 | 1515 | 0 | 0 | 0 | 0 |
124 | 1619 | 47 | 56 | 1563 | 9 | 0 | 9 | 19.15 |
202 | 2136 | 19 | 17 | 2115 | 0 | 2 | 2 | 10.53 |
205 | 2656 | 82 | 93 | 2563 | 8 | 3 | 11 | 13.41 |
209 | 3005 | 1 | 2 | 3003 | 1 | 0 | 1 | 100 |
210 | 2650 | 194 | 201 | 2449 | 5 | 2 | 7 | 3.61 |
212 | 2748 | 0 | 1 | 2747 | 1 | 0 | 1 | 100 |
213 | 3251 | 220 | 220 | 3031 | 0 | 0 | 0 | 0 |
215 | 3363 | 164 | 164 | 3199 | 0 | 0 | 0 | 0 |
217 | 2208 | 162 | 152 | 2036 | 3 | 7 | 10 | 6.17 |
220 | 2048 | 0 | 0 | 2048 | 0 | 0 | 0 | 0 |
221 | 2427 | 396 | 403 | 2024 | 6 | 1 | 7 | 1.77 |
223 | 2605 | 473 | 473 | 2132 | 0 | 0 | 0 | 0 |
228 | 2053 | 362 | 362 | 1691 | 0 | 0 | 0 | 0 |
230 | 2256 | 1 | 1 | 2255 | 0 | 0 | 0 | 0 |
231 | 1573 | 2 | 2 | 1571 | 0 | 0 | 0 | 0 |
234 | 2753 | 3 | 3 | 2750 | 0 | 0 | 0 | 0 |
36 | 80872 | 3408 | 5804 | 77366 | 50 | 48 | 98 | 2.87 |
Table 5 lists the processing speed analysis for each analyzed mother wavelet (db2, db4, coif6 and sym4) taking into account a half-hour record from MIT-BIH Arrhythmia Database. The processing time is computed in seconds.
Discussions
ECG analysis is an important issue related to healthcare, especially for telecardioloy applications. In this paper we presented a system based on Redundant Discrete Wavelet Transform (RDWT) associated with adaptive threshold methods for Premature Ventricular Contraction (PVC) detection with real-time approach.
There are several works that use the Wavelet Transform for ECG analysis, and the Wavelet family most used is the Daubechies family, especially the mother Wavelet db4 ( ^{Arrais et al., 2016} ; ^{Sasikala and Wahidabanu, 2010} ; ^{Singh and Tiwari, 2006} ). However, is not sure the choice for db4. In this paper was presented a comparative study between three Wavelet families and some of their mother wavelets: Daubechies (db2, db4, db6, db8, and db12), Coiflets (coif6, coif12 and coif18) and Symlets (sym4, sym6, sym8 and sym10). The Table 2 showed the comparative results.
The comparative study was based on standard deviation analysis between the ECG original signal energy and the scaling coefficients energy at all resolution level. It was analyzed around thirty recordings from MIT-BIH Arrhythmia Database as reference, which presents both ECG signal with and without PVC occurrence. The results showed that the low-order filters provide the best results for ECG analysis. This is a very interesting result, since the numerical processing time is directly proportional to the order filter, so low-order filters require less computational costs time.
It was verified that the best mother wavelet for ECG signal analysis is the db2 (Daubechies family. Furthermore, it can be observed that the Daubechies family provides the best results if compared to Coiflets wavelet family. However, comparing the Daubechies and Symlets family the results were very close, what was expected, since Symlets family is a modified version of Daubechies wavelets with increased symmetry. However, the Symlets family mathematical implementation is more complex if compared to Daubechies family.
It was observed that based on the energy of the wavelet coefficients and threshold methods can detect the occurrence of a premature ventricular contraction. Besides that, the energy wavelet coefficients provide the frequency band where the PVC energy present the most portion and the PVC duration time influence in the heartbeat. Thus, the frequency band can be used as indicative parameter of the ectopic stimulus origin ( ^{Malmivuo and Plonsey, 1995} ).
The database chosen for validated the algorithm is one of the most used for this propose. The Sensitivity (Se), Positive Predictivity (P^{+}) and Specificity (Sp) are the essentially parameters should be used to evaluate the performance results of arrhythmia detection algorithms ( ^{Kohler et al., 2002} ; ^{Martinez et al., 2004} ; ^{Wang, 2013} ). The Sensitivity (Se) indicates the algorithm’s ability to detect truly positive characteristics, therefore high Sensitivity indicates few false negative cases. The Positive Predictivity Value (P^{+}) indicates the algorithm’s ability to detect positive characteristics that are really positive, so the lower number of false positives provides the better algorithm positive predictability. The Specificity (Sp) indicates the algorithm’s ability to detect negative characteristics, therefore high Specificity indicates few false positive cases.
In general, Sensitivity and Specificity are the most indicated parameters for overall accuracy algorithm, whereas Sensitivity and Positive Predictivity Values are the indicated for algorithm performance measures ( ^{Wang, 2013} ). Therefore, based on these results it was found that there is a trade-off between the choice of wavelet filter order and the performance parameters. The high order wavelet filter presents a higher Sensitivity and Specificity if compared to low order filter, as verified between db2 and db4. Whereas the Positive Predictivity Value presents a high value for low order filter and low value for high order wavelet filter.
Although the db2 and db4 performance have been very close ( Table 3 ), it was chosen the db2 for proposed system, in order to achieve the best trade-off, with good Sensitivity, Positive Predictivity Value, Specificity and low order wavelet filter implementation algorithm. Through the Table 5 can verified that db2 presents the best speed performance. So, the db2 mother wavelet is the most indicated mother wavelet that provides reliable and accurate detection of the ECG signal characteristic.