Hilbert transforms and the equidistribution of zeros of polynomials

Carneiro, Emanuel; Das, Mithun Kumar; Florea, Alexandra; Kumchev, Angel V.; Malik, Amita; Milinovich, Micah B.; Turnage-Butterbaugh, Caroline; Wang, Jiuya

doi:10.1016/j.jfa.2021.109199

Cited by 10 publications

(1 citation statement)

References 15 publications

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“…where PV indicates the Cauchy's principle value integral. A detailed description of the HT is available in [20]. We compute the Hilbert PQ detection index (HPDI) by taking absolute values of HOM as detailed in the equation below.…”

Section: Hilbert Pq Detection Indexmentioning

confidence: 99%

Power Quality Detection and Categorization Algorithm Actuated by Multiple Signal Processing Techniques and Rule-Based Decision Tree

Singh¹,

Sharma²,

Garg³

et al. 2023

Sustainability

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This paper introduces a power quality (PQ) detection and categorization algorithm actuated by multiple signal processing techniques and rule-based decision tree (RBDT). This is aimed to recognize PQ events of simple nature and higher order multiplicity with less computational time using hybridization of the signal processing techniques. A voltage waveform with a PQ event (PQE) is processed using the Stockwell transform (ST) to compute the Stockwell PQ detection index (SPDI). The voltage waveform is also processed using the Hilbert transform (HT) to compute the Hilbert PQ detection index (HPDI). A voltage waveform is also decomposed using the Discrete Wavelet transform (DWT) to compute the classification feature index (CFI) [CFI1 to CFI4]. A combined PQ detection index (CPDI) is computed by multiplication of the SPDI, the HPDI and CFI1 to CFI4. Incidence of a PQE on a voltage signal is located with the help of a location PQ disturbance index (LPDI) which is computed by differentiating the CPDI with respect to time. CFI5, CFI6 and CFI7 are computed from the SPDI, the HPDI and the CPDI, respectively. Categorization of PQ events is performed using CFI1 to CFI7 by the rule-based decision tree (RBDT) with the help of simple decision rules. We conclude that the proposed algorithm is effective to identify the PQE with an accuracy of 98.58% in a noise-free environment and 97.62% in the presence of 20 dB SNR (signal-to-noise ratio) noise. Ten simple nature PQEs and eight combined PQ events (CPQEs) with multiplicity of two, three and four are effectively detected and categorized using the algorithm. The algorithm is also tested to detect a sag PQ event due to a line-to-ground (LG) fault incident on a practical distribution utility network. The performance of the investigated method is compared with a DWT-based technique in terms of accuracy of classification with and without noise, maximum computational time of PQ detection and multiplicity of PQE which can be effectively detected. A simulation is performed using the MATLAB software. MATLAB codes are used for modelling the PQE disturbances and the proposed algorithm using mathematical formulations.

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Section: Hilbert Pq Detection Indexmentioning

confidence: 99%