Sub-Nyquist Sampling and Parameters Estimation of Wideband LFM Signals Based on FRFT

Dong, Ningfei; Wang, Jianxin

doi:10.3103/s0735272718080010

Cited by 4 publications

(2 citation statements)

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“…As a generalized form of Fourier transform, Namias [ 37 ] redefined the concept of FrFT in a purely mathematical way from the perspective of eigenvalues and eigenfunctions, and gave a high-order differential form of FrFT in 1980. After Almeida [ 38 ] pointed out that FrFT can be understood as the rotation of the time–frequency plane, and Ozaktas [ 39 ] proposed a discrete algorithm with a calculation amount equivalent to FFT, more scholars have begun applying FrFT to the signal processing field [ 40 , 41 ]. The p -order fractional Fourier transform of a one-dimensional signal is defined as follows [ 42 ]:

where

is the kernel function, and its expression is

where

is the rotation angle, p is the order of the FrFT, and δ is the impulse function.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

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A New Method for Erosion Prediction of 90° Elbow Based on Non-Axisymmetric Ultrasonic-Guided Wave and the PSO–LSSVM Algorithm

Wang

Zhou

et al. 2023

Sensors

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The non-axisymmetric exciting guided wave can detect the thinning section of the elbow, and the time domain energy value of the signal collected at the outer arch position of the receiving end displays a downward trend as the remaining thickness of the erosion area decreases. To address the difficulty in detecting the erosion degree of the elbow with high accuracy, this paper uses the linear frequency modulation (LFM) signal to excite a non-axisymmetric guided wave that propagates in the 90° elbow and collects signals through four PZT receivers. To predict the erosion degree, the corresponding relationship between the energy value of the four signals after fractional Fourier filtering and the degree of elbow erosion is established through the particle swarm optimization (PSO)–least squares support vector machine (LSSVM) algorithm. The results show that the method proposed has an average accuracy rate of 98.1864%, 94.7167%, 99.119%, and 99.9593% for predicting the erosion degree of four elbow samples, and 94.0039%. and 81.2976% for two new erosion degrees, which are higher than the nonlinear regression model, LSSVM algorithm, and BP neural network algorithm. This study has guiding significance for real-time monitoring of elbow erosion.

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where

is the kernel function, and its expression is

where

is the rotation angle, p is the order of the FrFT, and δ is the impulse function.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Sensors 2023, 23, x FOR PEER REVIEW 3 of 17 scholars have begun applying FrFT to the signal processing field [40,41]. The p-order fractional Fourier transform of a one-dimensional signal is defined as follows [42]:…”

Section: The Frft Filtering Principle Of Lfm Signalmentioning

confidence: 99%