Construction of Wavelets

Sharma, Manish; Vanmali, Ashish V.; Gadre, Vikram M.

doi:10.1201/b16046-3

Cited by 12 publications

(6 citation statements)

References 23 publications

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“…It is a type of digital filter designed to have a specific frequency response. The frequency spread is a measure of the width of the filter's frequency response, and it is calculated by considering both the transition band and the pass/stopband of the filter [38]. The frequency spread design criterion is helpful because it takes into account the entire frequency spectrum of the filter rather than just the edge frequencies, which can be influenced by ripple amplitude specifications [39].…”

Section: B Orthogonal Filter Bank and Wavelet Decompositionmentioning

confidence: 99%

Automated Explainable Detection of Cyclic Alternating Pattern (CAP) Phases and Sub-Phases Using Wavelet-Based Single-Channel EEG Signals

et al. 2023

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Sleep is a crucial component of health and well-being. It maintains the metabolism of the body and covers one-third of total life. The assessment of sleep quality is typically done by evaluating the macrostructure-based sleep stages, however, it does not take into account transient phenomena like K-complexes and transient fluctuations, which are crucial for the diagnosis of various sleep disorders. Cyclic alternating pattern (CAP) is a recurrent physiological electroencephalogram (EEG) activity that takes place in the brain during sleep and it is considered as a microstructure of sleep that can provide more accurate and relevant evaluation of sleep. The traditional way of CAP phase division is done manually by sleep specialists, which is sensitive, time-consuming, and prone to inaccuracies. Hence, there is a need for automated detection techniques that can solve the problems. This study proposes an automated, computerized approach for developing a machine learning model with explainable artificial intelligence (XAI) capabilities, using wavelet-based Hjorth parameters for classifying CAP A & B phases and phases A sub-phases (A1, A2, A3). The study utilizes SHAP (SHapley Additive exPlanations)-based feature ranking to provide insights into the model. This study uses the publicly accessible Physionet CAP sleep database. The model is developed using single-channel standardized EEG recordings from healthy subjects and patients with five types of sleep disorders, namely, insomnia, nocturnal frontal lobe epilepsy (NFLE), periodic leg movement disorder (PLM), rapid eye movement behavior disorder (RBD) and narcolepsy. The best performance is obtained using k-nearest neighbors (KNN) and ensemble bagged trees (EbagT) classifiers. The proposed model achieved a average classification accuracy of 91.6% for healthy subjects and 94.33%, 86.3%, 88.68%, 84.43%, and 88.5% for narcolepsy, RBD, PLM, NFLE, and insomnia subjects respectively, for classifying phases A and B. Our model achieved a average classification accuracy of 92.85% for healthy subjects and 93.9%, 84.9%, 88.0%, 80.92%, and 89.41% for narcolepsy, RBD, PLM, NFLE, and insomnia subjects, respectively while categorizing A subphases (A1, A2, A3). The proposed method may help sleep experts to examine a person's sleep quality automatically using the microstructure of sleep.INDEX TERMS Cyclic alternating patterns (CAP), machine learning, electroencephalogram (EEG), phase A and phase B detection, k-nearest neighbor (kNN), sleep disorders.The associate editor coordinating the review of this manuscript and approving it for publication was Paolo Crippa .

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Section: B Orthogonal Filter Bank and Wavelet Decompositionmentioning

confidence: 99%

Automated Explainable Detection of Cyclic Alternating Pattern (CAP) Phases and Sub-Phases Using Wavelet-Based Single-Channel EEG Signals

et al. 2023

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“…The design problems of filter banks can be formulated as a constrained optimization problem (Sharma et al, 2014). The optimization problem minimizes or maximizes an objective function considering various design criteria such as passband and stopband ripples and errors, orthogonality, flatness at a particular frequency, regularity, phase response linearity, frequency selectivity, energy compaction, duration‐bandwidth localization (Sharma et al, 2013a). The selection of a particular criterion to design an optimal filter bank depends upon the application and signal to be processed (Bhati et al, 2016; Bhati et al, 2016; Sharma et al, 2015; Sharma et al, 2010; Sharma, Sharma, et al, 2019).…”

Section: Design Of Filter Banksmentioning

confidence: 99%

“…We have used a new class of orthogonal two‐channel filter bank, which is designed by converting the design problem into a constrained optimization problem (Sharma, Patel, & Acharya, 2021). Conventional orthogonal wavelet filter banks (Sharma et al, 2013a) are designed to have maximum number of vanishing moments. However, the filters do not provide any freedom for the optimization of the desired attribute of the filter.…”

Section: Design Of Filter Banksmentioning

confidence: 99%

“…Let

F ((), ζ)

be the

z

transform of the impulse response of the filter

f ((), n)

(Sharma et al, 2010; Sharma, Deb, & Acharya, 2018). In order to obtain a perfect reconstruction orthogonal filter bank, the following condition must be satisfied by the filter

F ((), ζ)

(Sharma, Agarwal, & Acharya, 2018),

F ((), ζ) F ((), ζ^{- 1}) goodbreak- F ((), goodbreak- ζ) F ((), goodbreak- ζ^{- 1}) goodbreak= 2 ζ^{- k}, k being odd

Then, the product filter can be defined as (Sharma et al, 2015):

H ((), ζ) goodbreak= ζ^{l} F_{0} ((), ζ) F_{0} ((), ζ^{- 1})

The orthogonality (2) condition can be expressed in terms of the halfband filter

H ((), ζ)

(Sharma, Tan, & Acharya, 2019) as

H ((), ζ) goodbreak+ H ((), goodbreak- ζ) goodbreak= 2

The halfband condition () condition can be expressed in the time domain (Sharma et al, 2013b; Sharma, Tan, & Acharya 2020) as:

\sum_{l = 0}^{k} f ((), l) f ((), l goodbreak- 2 n) goodbreak= δ ((), n); n goodbreak= 0, 1, \dots, \frac{k - 1}{2}

h ((), 2 n) goodbreak= δ ((), n)

The

M th ...

…”

Section: Design Of Filter Banksmentioning

confidence: 99%

“…The halfband condition (4) condition can be expressed in the time domain (Sharma et al, 2013b; Sharma, Tan, & Acharya 2020) as:…”

Section: Designmentioning

confidence: 99%

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Expert system for detection of congestive heart failure using optimal wavelet and heart rate variability signals for wireless cloud‐based environment

2021

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Congestive heart failure (CHF) is a cardiac disorder caused due to inefficient pumping of the heart, which leads to insufficient blood flow to the various parts of the body. The electrocardiogram (ECG) is widely used for the detection of heart diseases. However, it is prone to noise resulting in the detection of P, Q, R, S, and T waves ambiguous and erroneous. The heart rate variability (HRV) is considered to be a good indicator of various cardiac abnormalities. Hence, HRV is preferred. HRV can depict the magnitude of pumping of the heart in the RR interval signals accurately. This work proposes a method to automatically identify CHF using two‐band stopband energy (SBE) optimized orthogonal wavelet filter bank with HRV signals. In the proposed method, we have segmented the HRV data into lengths of 500 and 2000 samples. The HRV signals are decomposed into six sub‐bands, and the wavelet coefficients obtained are used for the extraction of fuzzy entropy (FE) and log energy (LE) features. The extracted features are utilized to classify HRV signals into control and CHF‐affected patients using support vector machine (SVM), bagged tree, complex tree, k‐nearest neighbour (KNN), and linear discriminant classifiers. The SVM performed better than other classifiers yielding the classification accuracy >95.20% and maximum classification accuracy of 99.30% with (2000 samples) using cubic SVM (CSVM). The 10‐fold cross‐validation method is employed during classification to reduce the over‐fitting phenomenon (Sharma, Dhiman, & Acharya, 2021). It appears that the proposed optimal wavelet‐based automated system can identify CHF accurately using HRV signals. Hence, the model may be applied in clinical usage during an emergency employing a cloud‐based wireless system after testing the developed model with more data.

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Signal Processing in Geosciences

Chandrasekhar

Ansari²

2022

Encyclopedia of Mathematical Geosciences

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Construction of Wavelets

Cited by 12 publications

References 23 publications

Automated Explainable Detection of Cyclic Alternating Pattern (CAP) Phases and Sub-Phases Using Wavelet-Based Single-Channel EEG Signals

Automated Explainable Detection of Cyclic Alternating Pattern (CAP) Phases and Sub-Phases Using Wavelet-Based Single-Channel EEG Signals

Expert system for detection of congestive heart failure using optimal wavelet and heart rate variability signals for wireless cloud‐based environment

Signal Processing in Geosciences

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