Sparse Discrete Fractional Fourier Transform and Its Applications

Liu, Shengheng; Shan, Tao; Tao, Ran; Zhang, Yimin D.; Zhang, Guo; Zhang, Feng; Wang, Yue

doi:10.1109/tsp.2014.2366719

Cited by 135 publications

(72 citation statements)

References 38 publications

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“…In the sparse representation process of ultrasonic phased array signal, the signal will be projected onto the orthogonal transform matrix. The commonly used orthogonal transform basis includes the discrete cosine transform basis, Fourier transform basis, wavelet basis, and curvelet basis [12][13][14][15].…”

Section: Reconstruction Of Ultrasonic Phased Array Signalmentioning

confidence: 99%

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Composite Plate Phased Array Structural Health Monitoring Signal Reconstruction Based on Orthogonal Matching Pursuit Algorithm

Sun

Wang

2017

Journal of Sensors

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In order to ensure the safety of composite components, structural health monitoring is needed to detect structural performance in real-time at the early stage of damage occurred. This is difficult to detect complex components with single sensor detection technology, so that ultrasonic phased array technology using multisensor detection will be selected. Ultrasonic phased array technology can scan the structure in all directions and angles without moving or less moving the probe and becomes the first choice of structural health monitoring. However, a large amount of data will be generated when using ultrasonic phased array with Nyquist sampling theorem for structural health monitoring and is difficult to storage, transmission, and processing. Besides, traditional Nyquist sampling cannot satisfy the sampling of large amounts of data without distortion, so a more efficient acquisition technique must be chosen. Compressive sensing theory can ensure that if the signal is sparse, it can be sampled in low sampling rate which is much less than two times of the sampling rate as defined by Nyquist sampling theorem for a large number of data and reconstructed in high probability. Then, the experiment result indicated that the orthogonal matching pursuit algorithm can reconstruct the signal completely and accurately.

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Section: Reconstruction Of Ultrasonic Phased Array Signalmentioning

confidence: 99%

“…Discrete Fourier transform (DFT) is a method that transforms the finite time domain data into the frequency domain data [13]. When a discrete time signal x n n = 0, 1, … , N − 1 with N sequence values is given, the following transform is the discrete Fourier transform of x n :…”

Section: Reconstruction Of Ultrasonic Phased Array Signalmentioning

confidence: 99%

Composite Plate Phased Array Structural Health Monitoring Signal Reconstruction Based on Orthogonal Matching Pursuit Algorithm

Sun

Wang

2017

Journal of Sensors

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“…According to the literature [10], the equation (4) is processed by a Fourier transform. We can obtain the fractional lower-order power spectrum of random signal p xy P .…”

Section: A Doppler Estimationmentioning

confidence: 99%

Parameter Estimation of Target in Interference Localization Background in Impulse Noise Environment

Li¹,

Shi²

2016

Proceedings of the 2016 International Conference on Automatic Control and Information Engineering

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Abstract-This paper proposes an airplane parameter estimation algorithm based on the study of the problem of interference localization in impulsive noise environment. Firstly, an extended signal model to accurately estimate parameters of the target is proposed with Alpha-stable distribution model. A method of Doppler estimation based on the peak of the fractional lower-order power spectrum is proposed. The 2D-FLOS-MUSIC algorithm is applied to estimate the azimuth angle and elevation angle. The correctness and effectiveness of the proposed method are verified with the computer simulation.

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“…Since DFrFT can transform a function to any intermediate domain between time and frequency domains, it exhibits superior capability to concentrate LFM signals with no effect from cross-terms. The continuous fractional Fourier transform is defined as (12), shown on the top of the page, where u denotes the fractional Fourier domain frequency, D is an integer, α denotes the rotation angle, and the phase of √ 1−j cot α is constrained in the range of (−π/4, π/4).…”

Section: Proposed Parameter Estimation Algorithmmentioning

confidence: 99%

A fast algorithm for multi-component LFM signal analysis exploiting segmented DPT and SDFrFT

Liu

Shan

Zhang

et al. 2015

2015 IEEE Radar Conference (RadarCon)

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This paper addresses the problem of estimating the chirp rates of multi-component linear frequency modulated signals, which is important in radar, sonar and navigation signal processing. The main difficulties in the estimation procedure lie in the cross-terms between multi-components and the high computation burden. To solve these problems, a novel algorithm that combines segmented discrete polynomial-phase transform and sparse discrete fractional Fourier transform is proposed to yield a significant reduction of the computational load with a satisfactory estimation performance. Simulation results are provided to demonstrate the effectiveness of the proposed approach.

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Sparse Discrete Fractional Fourier Transform and Its Applications

Cited by 135 publications

References 38 publications

Composite Plate Phased Array Structural Health Monitoring Signal Reconstruction Based on Orthogonal Matching Pursuit Algorithm

Composite Plate Phased Array Structural Health Monitoring Signal Reconstruction Based on Orthogonal Matching Pursuit Algorithm

Parameter Estimation of Target in Interference Localization Background in Impulse Noise Environment

A fast algorithm for multi-component LFM signal analysis exploiting segmented DPT and SDFrFT

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