Convolution and correlation theorems for Wigner–Ville distribution associated with the quaternion offset linear canonical transform

Bhat, M. Younus; Dar, Aamir H.

doi:10.1007/s11760-021-02074-2

Cited by 26 publications

(14 citation statements)

References 16 publications

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“…In [19] introduced the WVD association with the OLCT (WVD-OLCT), which is a generalization of the WVD-LCT and its special cases. Recently, in order to study higher dimensions, WVD associations with the quaternion LCT/OLCT were studied in [39][40][41][42], and WVD in the framework of octonion LCT was proposed by Dar and Bhat [43].…”

Section: Previous Resultsmentioning

confidence: 99%

Hybrid Transforms

Urynbassarova¹,

Urynbassarova²

2023

Time Frequency Analysis of Some Generalized Fourier Transforms

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Hybrid transforms are constructed by associating the Wigner-Ville distribution (WVD) with widely-known signal processing tools, such as fractional Fourier transform, linear canonical transform, offset linear canonical transform (OLCT), and their quaternion-valued versions. We call them hybrid transforms because they combine the advantages of both transforms. Compared to classical transforms, they show better results in applications. The WVD associated with the OLCT (WVD-OLCT) is a class of hybrid transform that generalizes most hybrid transforms. This chapter summarizes research on hybrid transforms by reviewing a computationally efficient type of the WVD-OLCT, which has simplicity in marginal properties compared to WVD-OLCT and WVD.

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Section: Previous Resultsmentioning

confidence: 99%

Hybrid Transforms

Urynbassarova¹,

Urynbassarova²

2023

Time Frequency Analysis of Some Generalized Fourier Transforms

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“…represents the space of all square integral functions on I. Thus, the condition for the existence of the sampling theorem for LCST, defined in (12), is proved.…”

Section: Sampling Theorem Of Lcstmentioning

confidence: 95%

“…Various types of transformations have been constructed using the LCT in recent times. For a further look at these constructions, we refer the readers to [7][8][9][10][11][12][13][14] and the references therein. We introduce the sampling theorem with error estimations in this work (based on the LCST).…”

Section: R G Stockwell Et Al Inmentioning

confidence: 99%

Sampling Techniques and Error Estimation for Linear Canonical S Transform Using MRA Approach

et al. 2022

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A linear canonical S transform (LCST) is considered a generalization of the Stockwell transform (ST). It analyzes signals and has multi-angle, multi-scale, multiresolution, and temporal localization abilities. The LCST is mostly suitable to deal with chirp-like signals. It aims to possess the characteristics lacking in a classical transform. Our aim in this paper was to derive the sampling theorem for the LCST with the help of a multiresolution analysis (MRA) approach. Moreover, we discuss the truncation and aliasing errors for the proposed sampling theory. These types of sampling results, as well as methodologies for solving them, have applications in a wide range of fields where symmetry is crucial.

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“…On the other hand, the application of signal processing-based algorithms for fault detection and isolation is discussed in refs. [ 17 , 18 , 19 ]. Furthermore, to design bearing fault diagnosis techniques, various approaches have been carried out that can be used in three main domains: the time domain, the frequency domain, and the time–frequency domain.…”

Section: Introductionmentioning

confidence: 99%

Bearing Fault Diagnosis Using a Hybrid Fuzzy V-Structure Fault Estimator Scheme

Piltan

Kim

2023

Sensors

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Bearings are critical components of motors. However, they can cause several issues. Proper and timely detection of faults in the bearings can play a decisive role in reducing damage to the entire system, thereby reducing economic losses. In this study, a hybrid fuzzy V-structure fuzzy fault estimator was used for fault diagnosis and crack size identification in the bearing using vibration signals. The estimator was designed based on the combination of a fuzzy algorithm and a V-structure approach to reduce the oscillation and improve the unknown condition’s estimation and prediction in using the V-structure method. The V-structure surface is developed by the proposed fuzzy algorithm, which reduces the vibrations and improves the stability. In addition, the parallel fuzzy method is used to improve the robustness and stability of the V-structure algorithm. For data modeling, the proposed combination of an external autoregression error, a Laguerre filter, and a support vector regression algorithm was employed. Finally, the support vector machine algorithm was used for data classification and crack size detection. The effectiveness of the proposed approach was evaluated by leveraging the vibration signals provided in the Case Western Reserve University bearing dataset. The dataset consists of four conditions: normal, ball failure, inner fault, and outer fault. The results showed that the average accuracy of fault classification and crack size identification using the hybrid fuzzy V-structure fuzzy fault estimation algorithm was 98.75% and 98%, respectively.

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Convolution and correlation theorems for Wigner–Ville distribution associated with the quaternion offset linear canonical transform

Cited by 26 publications

References 16 publications

Hybrid Transforms

Hybrid Transforms

Sampling Techniques and Error Estimation for Linear Canonical S Transform Using MRA Approach

Bearing Fault Diagnosis Using a Hybrid Fuzzy V-Structure Fault Estimator Scheme

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