Fourier-Bessel representation for signal processing: A review

Chaudhary, Pradeep Kumar; Gupta, Vipin; Pachori, Ram Bilas

doi:10.1016/j.dsp.2023.103938

Cited by 20 publications

(3 citation statements)

References 81 publications

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“…The roots of the first kind Bessel function of order-0 can be calculated using the technique described in Ref. 16 In general, the fringe signal is found to be effectively represented using few Bessel functions of first kind with order-0 with associated FBSE coefficients. This fact has been illustrated in the Fig.…”

Section: Two-dimensional Fourier-bessel Series Expansionmentioning

confidence: 99%

Fourier-Bessel series expansion-based fringe pattern denoising and inpainting

Kulkarni

2024

Optics and Photonics for Advanced Dimensional Metrology III

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The fringe pattern denoising and inpainting operations are crucial for the accurate phase retrieval in the phasebased optical measurement techniques. In this work, a Fourier-Bessel series expansion (FBSE)-based algorithm is proposed for the fringe pattern denoising and inpainting. The FBSE provides a compact representation of wide-band fringe pattern for the effective fringe signal denoising. The Bessel functions are used for the accurate reconstruction of non-stationary fringe signal even in the events of loss of fringe data at some object points. A comparative study between the FBSE, windowed Fourier filtering and partial differential equation-based methods is presented for the fringe pattern denoising. The simulation and experimental results indicate the suitability of the proposed method in practical applications.

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Section: Two-dimensional Fourier-bessel Series Expansionmentioning

confidence: 99%

Fourier-Bessel series expansion-based fringe pattern denoising and inpainting

Kulkarni

2024

Optics and Photonics for Advanced Dimensional Metrology III

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“…Filters can be classified into various types based on the filter approximation method, including Butterworth filters [38], Bessel filters [39], and Chebyshev filters [40]. Notably, the Butterworth filter is characterized by its uniformly flat amplitude-frequency traits within the passband and monotonically decreasing amplitude-frequency characteristics in the transition band.…”

Section: • Filter Selectionmentioning

confidence: 99%

Runway Pavement Structural Analysis Using Remote Laser Doppler Vibrometers

Yang,

Zhao,

Tian

et al. 2023

Applied Sciences

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Structural analysis is crucial for airfield pavement evaluation and plays a critical role in ensuring airfield operation safety and efficiency. Traditionally, the evaluation has relied on the Heavy Weight Deflectometer (HWD) test. This method encounters challenges, including interruptions in airfield operations, limited coverage of inspection locations, and extensive time required for data collection and analysis. In the presented research, a remote method for the measurement and analysis of runway pavement structural deflection induced by transiting aircraft was introduced, employing a Remote Laser Doppler Vibrometer (RLDV). First, a test system was developed to acquire deflection measurements of airport pavements using RLDV. To address inaccuracies arising from minor angle measurements and fixed-end beam vibrations, vibration correction methods were developed and validated. Thereafter, a linear regression model was constructed using data from both RLDV and HWD measurements, yielding a correlation coefficient of 0.94. This correlation highlights the reliable utility of RLDV in analyzing pavement structural response. The objective of this research is to present a novel approach for the evaluation of pavement structural performance.

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“…The proposed method allows the limitations of the Fourier analysis to be overcome. The Fourier analysis is based on time-frequency methods [7] that were used in the last few decades, namely the fractional [8][9][10], short time [11][12][13], windowed FT [14,15], Gabor [16][17][18], wavelet [19][20][21], Hilbert-Huang [22][23][24], and Fourier-Bessel transformations [25,26], and even decomposition over empirical modes [27,28].…”

Section: Introductionmentioning

confidence: 99%

Approximation of Aperiodic Signals Using Non-Integer Harmonic Series: The Generalized NAFASS Approach

2023

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In this paper, the non-orthogonal amplitude-frequency analysis of smoothed signals (NAFASS) method) is used to approximate discrete aperiodic signals from various complex systems with the non-integer harmonic series (NIHS). When approximating by the NIHS, there is a problem in determining the dispersion law for harmonic frequencies. In the original version of the NAFASS approach, the frequency dispersion law was determined from a linear-difference equation. However, many complex systems in nature have frequency distributions that differ from the linear law, which is used in the conventional Fourier analysis of periodic signals. This paper proposes a generalization of the NAFASS method for describing aperiodic signals by the NIHS with a frequency distribution that satisfies a recursive formula, which coincides with the local generalized geometric mean (GGM). The methodology of the generalized NAFASS method is demonstrated using descriptions of financial data (prices for metals) and sound data (sounds of insects) as examples. The results show the effectiveness of the generalized NAFASS approach for describing real-world time data. This discovery allows us to propose a new classification scheme for smoothed and aperiodic signals captured as responses and envelopes from various complex systems.

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Fourier-Bessel representation for signal processing: A review

Cited by 20 publications

References 81 publications

Fourier-Bessel series expansion-based fringe pattern denoising and inpainting

Fourier-Bessel series expansion-based fringe pattern denoising and inpainting

Runway Pavement Structural Analysis Using Remote Laser Doppler Vibrometers

Approximation of Aperiodic Signals Using Non-Integer Harmonic Series: The Generalized NAFASS Approach

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