Abstract

Introduction:

Heart disease is one of the leading causes of mortality worldwide, and early detection is crucial for effective treatment. Phonocardiogram (PCG) signals have shown potential in diagnosing cardiovascular conditions. However, accurate classification of PCG signals remains challenging due to high dimensional features, leading to misclassification and reduced performance in conventional systems.

Methods:

To address these challenges, we propose a Linear Vectored Particle Swarm Optimization (LV-PSO) integrated with a Fuzzy Inference Xception Convolutional Neural Network (XCNN) for early heart risk prediction. PC G signals are analyzed to extract variations such as delta, theta, diastolic, and systolic differences. A Support Scalar Cardiac Impact Rate (S2CIR) is employed to capture disease specific scalar variations and behavioral impacts. LV-PSO is used to reduce feature dimensionality, and the optimized features are subsequently trained using the Fuzzy Inference XCNN model to classify disease types.

Results:

Experimental evaluation demonstrates that the proposed system achieves superior predictive performance compared to existing models. The method attained a precision of 95.6%, recall of 93.1%, and an overall prediction accuracy of 95.8% across multiple disease categories.

Discussion:

The integration of LV-PSO with Fuzzy Inference XCNN enhances feature selection aPSO with Fuzzy Inference XCNN enhances feature selection and nd classification accuracy, significantly improving the diagnostic capabilities of PCG-classification accuracy, significantly improving the diagnostic capabilities of PCG-based systems. These results highlight the potential of the proposed framework as a based systems. These results highlight the potential of the proposed framework as a reliable tool for early heart disease prediction and clinical decision support.reliable tool for early heart disease prediction and clinical decision support.

1 Introduction

One of the leading causes of death globally is heart disease, impacting human life due to clinical identification errors resulting in increased fatalities. Early prediction and data analysis are essential in reducing the risk of patient outcomes and efficiently analyzing data (Bourouhou et al., 2019; Vahanian et al., 2021). Most existing techniques must concentrate on the disease properties and feature dimension in the intake data analysis structure (Er, 2021). So, increasing variations in feature analysis takes more dimension to produce poor accuracy in the sense of low precision, recall rate, and F1 measure on various parameters.

By considering the problematic issues, the optimization must improve the feature selection and classification for extraordinary outcomes (Schmidt et al., 2010; Deng et al., 2020). Cardiovascular disease is the leading cause of death worldwide, affecting millions of people annually with a variety of heart conditions. Patients must receive timely and efficient treatment for heart disease if early detection and correct diagnosis are to be achieved. Furthermore, Machine Learning (ML) algorithms provide significant assurance in clinical diagnosis, specifically in heart sound classification for diagnosing cardiac diseases (Shuvo et al., 2021).

Furthermore, many abnormalities, such as heart murmurs and artifacts associated with cardiovascular disease, can affect the heart rate, which is the most common cause of death. Thus, they offer a new method for early detection of heart disease (Shuvo et al., 2023; Dhiyanesh et al., 2024). Afterward, feature vectors can be generated by extracting features from the inputs acquired directly from the heart sounds using a Deep Neural Network (DNN) algorithm. Moreover, the efficacy of the suggested approach can be evaluated in a real-world setting (Springer et al., 2015).

A promising method for classifying heart sounds involves analyzing recordings of sounds created by the heart during each cardiac cycle using PCG signals. Figure 1 describes the Working Principle of PCG Signal Observation and Processing. These signals contain valuable information about heart function and can be analyzed using DL techniques to identify patterns associated with different heart states (Waaler et al., 2023). In this paper, we present future work to improve the classification of heart diseases by utilizing a combination of Linear Vector Particle Swarm Optimization (LVPSO) and Xception Convolutional Neural Networks (XCNN). In the first step, the PCG signal can be pre-processed using the proposed methods to extract the relevant features for classification. This includes techniques such as signal elimination, segmentation, and feature extraction to improve data quality and reduce noise and artifacts that can interfere with classification. Once the data is pre-processed, it can be input into the LVPSO algorithm. The LVPSO algorithm is a variation of the traditional particle swarm optimization algorithm designed for linear vector optimization problems.

Working principle PCG signal observation and processing.

The LVPSO algorithm works by repeatedly updating the number of candidate solution particles based on the fitness values of the sound signal, which are determined by a linear vector objective function. This enables the algorithm to search the solution space efficiently and find the optimal parameters for the classification task. Using LVPSO, hyperparameters of Xception CNN, such as learning rate, block size, and number of layers, can be effectively modified to increase the accuracy of the classification model. Xception CNN, a DL framework, has demonstrated outstanding performance in classification tasks and has recently been utilized in clinical signal analysis with optimistic results. By combining Xception CNN with LVPSO, we aim to leverage the strengths of both algorithms to improve the accuracy and robustness of cardiovascular disease classification models. This collaborative approach, where the Xception CNN will be trained on the pre-processed PCG signals to understand the underlying patterns associated with different heart states and the LVPSO will optimize the CNN, invites all of us to be part of this exciting journey toward better understanding and classifying cardiovascular diseases hyperparameters.

The proposed acoustic classification of cardiac disease using LVPSO and exception CNN has the potential to significantly enhance the accuracy and efficiency of cardiac disease diagnosis. By leveraging the power of ML algorithms and DL frameworks, a robust and reliable classification model can be developed to assist healthcare professionals in the early detection and treatment of cardiac disorders. However, it is crucial to note that further research and experiments are essential to validate the efficacy of this approach. The initial results are promising, suggesting that this approach could have a significant impact on the field of heart disease.

The paper is structured into several sections to outline the cardiac sound classification research process. Section 1 provides an introduction to the research; Section 2 reviews the principles of existing methods along with their pros and cons; Section 3 explains the proposed method; Section 4 presents method comparisons; and Section 5 concludes with a discussion and final remarks, highlighting the performance of the proposed work and suggesting future developments.

2 Related work

A recent literature review (Krishnan et al., 2020) comprehensively summarizes current research on using PCG signals in predicting cardiac diseases through ML and DL methods. The potential of advanced technologies like ML and artificial intelligence to significantly enhance the precision and effectiveness of cardiac disease prediction is gaining momentum. Cardiovascular disease, a leading global cause of mortality, underscores the importance of timely identification for successful intervention and prevention. Recent analyses through various signal transformations have highlighted the importance of predicting heart disease by audio signals (Kiranyaz et al., 2020). Analyzing heart sounds with a phonocardiograph allows for recording heart sounds, which can be further explored with computational algorithms.

Early identification of abnormal heart sounds is a significant challenge in predicting heart disease. Conventional diagnostic methods for heart disease, like Electrocardiograms (ECG), are usually invasive and require specialized approaches. However, the use of non-invasive tools like stethoscopes to gather sound signals offers a convenient and promising approach to predicting heart disease.

Recent technological advances have enabled the characterization of DL heart disease based on PCG signals (Dhiyanesh et al., 2025). Modern DL methods, such as CNNs and Recurrent Neural Networks (RNNs), have successfully identified inconsistencies in PCG data. The potential of these advanced methods to revolutionize early detection and diagnosis of heart disease, reduce the burden on healthcare facilities, and improve patient outcomes is significant. However, a substantial problem with PCG signal processing is the different limitations on feature selection. The dimensionality of breeding features often leads to incorrect feature selection and poor accuracy.

The novel proposed that the prediction accuracy of heart failure can be improved by combining neural networks and Particle Swarm Optimization (PSO) techniques. However, cardiovascular disease continues to be a significant issue globally, with its mortality rate on the rise (Mahalakshmi and Rout, 2023).

Moreover, the enhanced PSO algorithm identifies the optimal features and feature subsets. The optimal feature subset is carefully selected and fed into an ensemble classifier to determine the likelihood of heart disease accurately (Yuliandari et al., 2024). A new approach to a Neural Fuzzy Inference System (NFIS) for representing training data can be created using n-dimensional functions. NFIS optimizes learning algorithms by calibrating them with an error calculation module (Jha et al., 2022). The new approach aimed to detect cardiac disorders using health metrics gathered from wearable sensors integrated with a Fuzzy Logic Inference System (FLIS) (Kadu et al., 2022).

Furthermore, CNNs are extensively employed to predict heart disease in various domains, including computer vision and image identification. CNNs can accurately assist in analyzing and predicting heart disease. Furthermore, CNNs can automatically learn hierarchical representations of data (Alzubaidi et al., 2021).

PSO-based methods can be applied to optimize the parameters of stacked sparse autoencoders. Furthermore, PSO optimization permits enhancing the performance of feature learning and classification (Mienye and Sun, 2021).

Table 1 presents DL techniques, datasets, and methods derived from previous approaches for heart disease detection, outlining the constraints and accuracy of performance evaluation achieved in predicting heart diseases.

ReferencesClassification methodDatasetLimitationPerformance evaluationAccuracyNaveenkumar et al. (2022)CNN-based Xception Network (CNN-XN)Heart soundThe number of deaths caused by CVD is on the rise across the globe.Accuracy, precision94.52%Nwonye et al. (2021)CNNCoronary heart diseaseInactivity and unhealthy fitness can also increase the risk of CVDSensitivity, accuracy85.79%Fu et al. (2020)Multi-Scale CNN with Attention Mechanisms (MSCNN-AM)Benchmark datasetsThe blood vessels exhibit changes in their shape and show reduced variability.Specificity, F1-score0.83%Gárate-Escamila et al. (2020)Chi-square- principal component analysisUCI ML repositoryHowever, the classification of CVD can often be unbalanced.Matthews correlation coefficient85.67%(Yang and Guan 2022)Synthetic Minority Overestimation Technique (SMOTE)Heart diseaseCVD reduces the accuracy and effectiveness of clinical diagnostic data.False positive rate, true positive rate92.44%

Heart disease detection based on deep learning (DL) technique.

The proposed method utilizes SMOTE to manage imbalanced data in datasets effectively. Besides, these permit accurate classification of a given dataset and ensure maximum accuracy in performance evaluation results (Waqar et al., 2021). Cardiac signals can be automatically detected by decomposing them into discrete model functions utilizing the Complete Ensemble Empirical Mode Decomposition (CEEMD) method (Manuel Centeno-Bautista et al., 2023). Moreover, the signal-to-noise ratio model parts can be approximated to extract time and frequency details of the decaying mode through the EEMD analysis method (Zhao et al., 2023). Hence, the Least Mean Square (LMS) algorithm offers an optimal adaptive filter system for accurately estimating noisy signals. Likewise, a noisy signal can be processed in series with multiple adaptive filter stages (Hannah Pauline and Dhanalakshmi, 2022).

Furthermore, DL techniques have analyzed the ability to predict heart disease from sound signals. For example, Raza et al. (2019) developed a CNN-based model that detects heart murmurs from acoustic signals with up to 90% accuracy. Similarly Jones et al. (2019), used RNN to predict the onset of atrial fibrillation with an accuracy of 85%. Furthermore, DL techniques such as CNN and RNN have indicated accurate results in analyzing sound signals to predict heart disease. While RNNs are more effective at collecting temporal correlations in data, CNNs are better at extracting spatial features from sound recordings. By combining the two techniques, researchers achieved greater accuracy in predicting various heart diseases. However, feature dimensionality creates worst-case scenarios during classification, as threshold changes in feature ranges can lead to lower precision and recall.

In addition to CNNs and RNNs, auto-encoders and Generative Adversarial Networks (GANs) are other DL techniques studied to predict cardiac disease in sound signals. For example Ramkumar et al. (2024), proposed a GAN-based model for generating artificial heart sounds to improve the training data and prediction accuracy. However, the parametric performance reduces the accuracy and results in a high error rate due to high time complexity and uncorrelated feature analysis.

The literature on predicting cardiac disease using DL techniques on sound signals still needs to be improved. Furthermore, these models focus more on large-scale analysis of populations in real-world clinical settings to ensure their effectiveness. In Amiriparian's et al. (2019) study, the authors proposed a DL model to classify heart sounds into different categories, including standard and abnormal. The model achieved high accuracy in differentiating various types of heart sounds and demonstrated the potential of DL in analyzing sound signals for heart disease prediction. Another study by Li H. et al. (2020) focused on using DL for early detection of heart murmurs. The authors have developed a DNN that can accurately classify heart murmurs based on acoustic signals, showing promising results for early diagnosis of heart disease.

In a review by Wang J. et al. (2018), the authors discussed the various DL techniques used in heart disease prediction, including CNNs and RNNs. The review highlighted the crucial role of sound signals in improving the accuracy of prediction models, ensuring the audience is well-informed about the key factors in heart disease detection.

Among the seminal works in the field (Yang et al., 2021) proposed a DL model for cardiac disease prediction using acoustic signals conducted. The results demonstrate a capable accuracy in diagnosing heart disease and highlight the potential of the DL technique. Based on sound signals, a DL model for the prediction of cardiac disease was established by another critical analysis (Li Y. et al., 2020). The author combined a CNN with a Long Short-Term Memory (LSTM) algorithm to accurately predict cardiac illness by analyzing auditory data. Furthermore, they demonstrate the effectiveness of combining different DL frameworks to improve forecasting performance. In addition to these studies, several research papers have investigated using DL techniques for heart disease prediction using audio signals. For example, Wang H. et al. (2018) proposed an RNN-based DL model for heart disease prediction, and Gomathi et al. (2024) used a hybrid DL model combining CNN and SVM for the same objective.

Furthermore, researchers have analyzed using transfer learning in heart disease prediction with sound signals. For example, Hettiarachchi et al. (2017) applied knowledge from pre-trained DL models to enhance heart disease prediction performance, showcasing the potential of transfer learning in this area. Bentley et al. (2011) assembled a PASCAL dataset of heart sounds from patients with and without heart disease and used a CNN for sound signal classification. The University of Michigan Health System presents the Murmur Database (MHSTP), comprising 23 heartbeat recordings computing 1496.8 s. In the CEEMD, murmurs in heart sound signals are detected. CEEMD is University of Michigan Health System (2015) more advanced than EMD as it solves the mode mixing issue present in EMD. Extraction of the murmur and heart sounds using composting methods such as EMD has been performed (Oliveira et al., 2021; Dhiyanesh et al., 2024). In general, Ali et al. (2023) using DL methods to examine sound signals for predicting cardiac diseases shows significant potential in enhancing early detection and treatment results, thereby improving patient outcomes. By employing artificial intelligence capabilities, researchers can create more precise and effective predictive models to support healthcare providers in delivering improved care to individuals with heart diseases.

Table 2 shows the proposed method derived from previous studies, describing its limitations and limitations. Furthermore, they can be tested in feature selection methods for predicting heart disease. The techniques listed in the table provide a systematic approach to selecting relevant features important for accurate heart disease prediction.

ReferencesResearch gapMethodologyFeature usedProblemsDewangan et al. (2008)Only covers time depends on the feature, not the actual limits of the featureDiscrete Wavelet Transform (DWT)Time series DWTECG recordings are insufficient to reveal valve health information.Schanze (2017)ML and DL concepts for feature evaluation generate errorsSingular Value Decomposition (SVD)SVD, mean filtersTransformation methods eliminate unwanted signal componentsOthman and Khaleel (2017)Time feature limits discover the coefficient dependencies of feature limits.Fast Fourier Transform (FFT)Shanon energy, DWTDiscovering the most efficient approach will require a significant amount of time.Martinek et al. (2017)Non-real feature limits cannot take the acoustic valuesLMSAdaptive mean filters and statistical featuresA standard channel is necessary for fiber optic interferometry.Rao (2019)All feature limits and dimension forumsFinite Impulse Response (FIR)Bimedical signal peak signal tupe featuresHowever, measuring digital signals as discrete signal phases, such as time or amplitude, is necessary.Sh-Hussain et al. (2016)Statistcal part of frequencies are missing absolute valuesMel-Frequency Ceptrum Coefficients (MFCCs)Alpha feature limitsCVD is one of the most severe illnesses that can lead to death.VenkataHari Prasad and Rajesh Kumar (2015)PCG signals are not supportedDWTTime domain featuresAn ECG recording alone cannot provide information regarding the health of the valves.Pan et al. (2015)Real-time dataset series are not supported. Unconsistent margins are taken, and actual values are uncovered.Backpropagation Algorithm (BPA)Wavelet featuresLow-level data on the determinationLubaib and Ahammed Muneer (2016)Least level margins of signals only supportK Nearest Neighbor (KNN)Subset carinal featuresInterpreting a PCG typically necessitates a proficient and seasoned practitioner.Zubair (2021)Utilizing the publicly available PhysioNet/Cinc Challenge 2016 database.Multi-Layer Perceptron (MLP)Mel frequency Cepstral Coefficients (MFCC)Computational complexity rises when heart sounds are classified as normal or abnormal.

The research gap in the feature selection method used for predicting heart disease.

Some effective models can classify PCG signals using Attention-Based Bidirectional LSTM (A-BLSTM) techniques (Prabhakar and Won, 2023). Another study used (Sivakami and Prabhu, 2023) Cuckoo Search Bio-inspired Algorithm (CSBA) with DBN method for heart disease prediction. Similarly, the novel Muthulakshmi and Parveen (2023) developed a Z-score normalization, African Buffalo Optimization (ABO) methods for effective disease prediction. Study Taylan et al. (2023) concentrated on classification of cardiovascular disease with the help of support vector regression (SVR) and ANFIS algorithm. Similarly, the article Thakkar and Agrawal (2023) used a deep CNN and min-max normalization method. The novel Yusuf Ilu and Prasad (2023) introduced an autoregressive integrated moving average (ARIMA) and K-means Clustering methods for disease identification. The literature review indicates a rising interest in applying DL techniques for predicting cardiac disease based on audio signals. Various studies reviewed in this research have demonstrated the efficiency of DL models such as CNN, LSTM, and RNN in accurately predicting cardiac disease from audio signals. Besides, investigating transfer learning and hybrid models exhibits potential for further advancement in this field. In conclusion, exploring heart disease predictions through DL techniques using sound signals holds great promise in improving early detection. Through employing the capabilities of DL, researchers can create precise and effective predictive models that have the potential to save lives.

2.1 Problem identification factors and consideration

From the literature, we found the complex nature of heart disease prediction based on sound signals having difficulties.

One of the critical issues in PCG signal processing is the potential for improper feature selection due to identical feature dimensions. This can significantly undermine the accuracy of the results, leading to poor outcomes. Feature dimensionality creates worst-case scenarios during classification because the range variation in feature ranges causes low precision and recall rates.

The previous methods' simulation parameters degraded the performance accuracy, so it has a higher false rate due to non-relation feature analyses, more time complexity, and higher error rates.

2.2 Research gap

A significant research gap exists in the understanding of complex features extracted from phonocardiogram (PCG) signals that can be used to predict cardiac disease.

Including only time depends on the feature, not the actual limits of ML and DL concepts for feature estimation.

The previous algorithms are insuufficiently focus herat disease early stage prediction and One of the reaserch gap in cardiovascular disease diagnosis is the quality of the analytical data. ECG and PCG signals are sensitive to noise and artifacts. The amount of data generated can be enormous, making it difficult to effectively manage this data for signal processing and interpretation, and researchers are continuously working to develop powerful techniques to reduce noise and improve signal quality.

Missing data values will result in errors; Valueless data is fuzzy because it can be either true or false. Decision-making ability depends on the quality of data. Small improvements in data dimension can lead to large improvements in decision-making information.

3 Proposed methodology

Toward developing a Linear Vectored-Particle Swarm Optimization based on Fuzzy Inference Xception Convolution Neural Network for early heart risk prediction. The first step in this approach is to utilize the Pascal dataset, which contains valuable information in the form of PCG representation. PCG signal format is used to convert sound waves into data, allowing for the identification of critical features such as Delta, Theta, diastolic, and systolic differences present in the dataset. These factors significantly influence the risk of heart disease. The model accuracy is improved by applying preprocessing techniques such as SMOTE and EDAMF to cardiac clinical data. These techniques help normalize the data and address balances or inconsistencies present in the dataset, ultimately improving the overall model's overall performance.

To identify the scalar differences based on disease properties and assess the behavioral impact, a Support Scalar Cardiac Impact Rate (S2CIR) is utilized. This metric helps understand the disease's severity and impact on the individual, providing valuable insights for early detection and intervention. Figure 2 shows the Proposed LVPSO-FIXCNN Workflow Architecture Diagram. Notably, the Multivariate disease impact rate is used to determine the non-linearity scaling values, a crucial step in our research. These values are then processed using Linear Vectored–Particle Swarm Optimization (LV-PSO) for feature selection and dimensionality reduction, enhancing the model's performance and ensuring that only the most pertinent features are utilized for predictions.

Proposed LVPSO-FIXCNN workflow architecture diagram.

Finally, the selected features are trained using a Fuzzy Inference Xception Convolution Neural Network (FIXCNN) to categorize the type of heart disease and provide accurate predictions. FIXCNN models utilize the capabilities of DL and fuzzy logic to examine intricate patterns in data and generate well-informed decisions, resulting in enhanced precision and dependability of predictions.

The heart PCG signals consist of several frequency components corresponding to different cardiac cycle physiological events, as indicated in Figure 3. The frequency range of cardiac sound waves is displayed in Table 3. The closure of the tricuspid and mitral valves produces the first heart sound (S1), which has low-frequency features. The closure of the aortic and pulmonary valves results in the second heart sound (S2), which has a higher frequency component.

Heart sound PCG amplitude signal.

Frequency of sound signal levelsFrequency limits in HzInitial amplitude sector [S1] [S2]Max-frequency energy strengthSystolic signal variation ≤ 30++, ≤ 100 Hz100≥, ++ HzPost amplitude sector [S3] [S4]Min frequency energy strengthDiastolic signal variation20 ≤ , 25 Hz≥30 Hz

Levels of heart sound signal frequency limits.

Two additional heart sounds, S3 and S4, may indicate abnormal heart activity. The timing and intensity of cardiac PCG signals provide valuable information on the cardiac cycle. The heart sounds S1 to S2 are called the systolic interval, indicating the ventricular contraction and ejection length. The intensity of heart sounds may fluctuate due to factors like ventricular contraction and valve abnormalities. Changes in timing and intensity can indicate conditions such as heart failure or valvular stenosis.

3.1 Synthetic Minority Oversampling Technique (SMOTE)

In this section, a training dataset is developed using SMOTE to predict heart disease. Furthermore, leveraging the SMOTE technique can find extensive applications in the healthcare sector for managing class-imbalanced data. Then, by utilizing Euclidean distance to create synthetic generated random data of minority classes from nearby neighbors, the number of data instances can be enhanced. Moreover, new samples are generated by leveraging the top features from the original data. The SMOTE technique can produce optimal values of the application, thereby introducing additional noise. By oversampling minority classes, synthetic samples are created by adding line segments from the k nearest neighbors of the minority class to each sample. Neighbors can be selected randomly from the k nearest neighbors based on oversampling as required. A synthetic model is also created to predict the differences between the analyzed feature vector model and its nearest neighbors. Moreover, the feature vectors are evaluated with 0 and 1, multiplying their variances by random numbers.

Creating synthetic data from minority classes of random number data can be achieved by calculating population functions. Furthermore, nearest neighbors provide new index array features for different samples, as detailed in Algorithm 1. Let's assume the id-number of the synthetic sample, Z-Minority instance, K-nearest neighbor, x- integral sample, du−number of the attribute, W-sample, q−populate, Ww−synthetic sample, Dd−nearest neighbor, dx−new index, xu−attribute index, α−random number.

Table 4 compares the performance of different variation methods like Support Vector Regression (SVR) and Autoregressive Integrated Moving Average (ARIMA). The proposed method attains 80.98%, 84.09%, and 90.21% for Pascal, Circor and Physico-cardnet, respectively.

Methods/datasetsSVRARIMASMOTEPascal67.1574.0980.38Circor73.6278.1084.09Physico- cardnet79.3580.5490.21

Comparison performance for variations methods.

3.2 Enhanced empirical mode decomposition adaptive filter

In this section, advanced empirical methods enable the analysis of time-domain or one-dimensional signals through an adaptive filter technique. The EEMDAF method is also known for decomposing a one-dimensional signal into different Eigenmode functions and frequency bands using frequency information. Also, the number and intensity of zero crossings in the 1D signal in the intrinsic mode functions must be different or equal. The estimated mean value will be zero when using symmetrical lower and upper envelopes. The process is repeated until all accurate Eigenmode functions are computed using the analytical EEMDAF method.

Moreover, filter integration approximates the input-output relationship of the EEMDAF method. By considering only current and past observations, the weighting of adaptive filters can produce statistically better estimates of the following observations.

Furthermore, the EEMDAF technique removes reference signal interference from the cross-correlation matrix and ensures vector independence. Noise estimation also includes estimating signals from the power supply and other known noise sources. Unlike frequency-selective filters, adaptive filters use an autocorrelation matrix instead of a crucial input to normalize the most and least significant engine values.

Lower and upper envelopes are estimated using cubic splines connecting the determined local maximum and minimum points, as described in Equation 1. Let's assume new 1D signal, the iz−minimum and maximum point of the 1D signal, and the mean of both envelopes.

Equation 2 approximates the new 1D signal's local maximum and minimum points. Compute the residual signal subtracted from the 1D signal and evaluate the Eigen mode function as shown in Equation 3. Where residual signal, IMF1−intrinsic mode functions, condition signal.

Calculate the final residual signal of the Eigen mode function derived from the initial 1D signal, as indicated in Equation 4.

Compute a new 1D signal from the Gaussian white noise sequence shown in Equation 5. Where c-trials, dx(z)−Gaussian noise series, ix(z)−initial 1D signal.

Evaluate the Eigen mode function of the frequency band as described in Equation 6. Let's assume EEMD−ensemble empirical mode decomposition, x, y-identified by frequency band. M-complete ensemble.

The adaptive filter used for filtering is calculated at the beginning of the procedure described in Equation 7. Where i[d]−uncorrelated with a reference signal, D-Noise, Pcg −Phonocardiogram.

Adaptive filters are standard and have a straightforward cost function. They generate a quadratic cost function with a global minimum for noise filtering. Calculate the noise in the reference signals between the auto-correlation matrix and cross-correlation vectors, as shown in