• Title/Summary/Keyword: fractional Fourier transform

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LFM Signal Separation Using Fractional Fourier Transform (Fractional Fourier 변환을 이용한 LFM 신호 분리)

  • Seok, Jongwon;Kim, Taehwan;Bae, Keunsung
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.17 no.3
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    • pp.540-545
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    • 2013
  • The Fractional Fourier transform, as a generalization of the classical Fourier Transform, was first introduced in quantum mechanics. Because of its simple and useful properties of Fractional Fourier transform in time-frequency plane, various research results in sonar and radar signal processing have been introduced and shown superior results to conventional method utilizing Fourier transform until now. In this paper, we applied Fractional Fourier transform to sonar signal processing to detect and separate the overlapping linear frequency modulated signals. Experimental results show that received overlapping LFM(Linear Frequency Modulation) signals can be detected and separated effectively in Fractional Fourier transform domain.

ON UNIFORM SAMPLING IN SHIFT-INVARIANT SPACES ASSOCIATED WITH THE FRACTIONAL FOURIER TRANSFORM DOMAIN

  • Kang, Sinuk
    • Honam Mathematical Journal
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    • v.38 no.3
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    • pp.613-623
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    • 2016
  • As a generalization of the Fourier transform, the fractional Fourier transform plays an important role both in theory and in applications of signal processing. We present a new approach to reach a uniform sampling theorem in the shift-invariant spaces associated with the fractional Fourier transform domain.

GENERALIZED PSEUDO-DIFFERENTIAL OPERATORS INVOLVING FRACTIONAL FOURIER TRANSFORM

  • Waphare, B.B.;Pansare, P.D.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.1
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    • pp.105-115
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    • 2021
  • Generalized pseudo-differential operators (PDO) involving fractional Fourier transform associate with the symbol a(x, y) whose derivatives satisfy certain growth condition is defined. The product of two generalized pseudo-differential operators is shown to be a generalized pseudo-differential operator.

A GENERALIZED APPROACH OF FRACTIONAL FOURIER TRANSFORM TO STABILITY OF FRACTIONAL DIFFERENTIAL EQUATION

  • Mohanapriya, Arusamy;Sivakumar, Varudaraj;Prakash, Periasamy
    • Korean Journal of Mathematics
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    • v.29 no.4
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    • pp.749-763
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    • 2021
  • This research article deals with the Mittag-Leffler-Hyers-Ulam stability of linear and impulsive fractional order differential equation which involves the Caputo derivative. The application of the generalized fractional Fourier transform method and fixed point theorem, evaluates the existence, uniqueness and stability of solution that are acquired for the proposed non-linear problems on Lizorkin space. Finally, examples are introduced to validate the outcomes of main result.

Estimation of target distance based on fractional Fourier transform analysis of active sonar linear frequency modulation signals (능동소나 linear frequency modulation 신호의 fractional Fourier transform 분석에 기반한 표적의 거리 추정)

  • Hyung, Sungwoong;Park, Myungho;Hwang, Soobok;Bae, Keunsung
    • The Journal of the Acoustical Society of Korea
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    • v.35 no.1
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    • pp.8-15
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    • 2016
  • As a generalized form of the conventional Fourier transform, fractional Fourier transform (FrFT) can analyze a signal at intermediate domain between time and frequency domains with a transform order ${\alpha}$. Especially, FrFT has a number of advantages in the analysis of LFM (Linear Frequency Modulation) signals due to its robustness to noise. In this paper, we have proposed a new method to detect and estimate the distance of the target from the FrFT spectrum of the received echo signal. Experimental results have validated the proposed method, and shown that reliable target distance could be estimated in noise and reverberation environments.

On Narrowband Interference Suppression in OFDM-based Systems with CDMA and Weighted-type Fractional Fourier Transform Domain Preprocessing

  • Liang, Yuan;Da, Xinyu;Wang, Shu
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.11 no.11
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    • pp.5377-5391
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    • 2017
  • In this paper, we propose a new scheme to suppress the narrowband interference (NBI) in OFDM-based systems. The scheme utilizes code division multiple access (CDMA) and weighted-type fractional Fourier transform (WFRFT) domain preprocessing technologies. Through setting the WFRFT order, the scheme can switch into a single carrier (SC) or a multi-carrier (MC) frequency division multiple access block transmission system. The residual NBI can be eliminated to the maximum extent when the WFRFT order is selected properly. Final simulation results show that the proposed system can outperform MC and SC with CDMA and frequency domain preprocessing in terms of the narrowband interference suppression.

Active Sonar Target Detection Using Fractional Fourier Transform (Fractional 푸리에 변환을 이용한 능동소나 표적탐지)

  • Baek, Jongdae;Seok, Jongwon;Bae, Keunsung
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.20 no.1
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    • pp.22-29
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    • 2016
  • Many studies in detection and classification of the targets in the underwater environments have been conducted for military purposes, as well as for non-military purpose. Due to the complicated characteristics of underwater acoustic signal reflecting multipath environments and spatio-temporal varying characteristics, active sonar target detection technique has been considered as a difficult technique. In this paper, we describe the basic concept of Fractional Fourier transform and optimal transform order. Then we analyze the relationship between time-frequency characteristics of an LFM signal and its spectrum using Fractional Fourier transform. Based on the analysis results, we present active sonar target detection method. To verify the performance of proposed methods, we compared the results with conventional FFT-based matched filter. The experimental results demonstrate the superiority of the proposed method compared to the conventional method in the aspect of AUC(Area Under the ROC Curve).

Active Sonar Target Recognition Using Fractional Fourier Transform (Fractional Fourier 변환을 이용한 능동소나 표적 인식)

  • Seok, Jongwon;Kim, Taehwan;Bae, Geon-Seong
    • Journal of the Korea Institute of Information and Communication Engineering
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    • v.17 no.11
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    • pp.2505-2511
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    • 2013
  • Many studies in detection and classification of the targets in the underwater environments have been conducted for military purposes, as well as for non-military purpose. Due to the complicated characteristics of underwater acoustic signal reflecting multipath environments and spatio-temporal varying characteristics, active sonar target classification technique has been considered as a difficult technique. And it has difficulties in collecting actual underwater data. In this paper, we synthesized active target echoes based on ray tracing algorithm using target model having 3-dimensional highlight distribution. Then, Fractional Fourier transform was applied to synthesized target echoes to extract feature vector. Recognition experiment was performed using neural network classifier.

Multi-aspect Based Active Sonar Target Classification (다중 자세각 기반의 능동소나 표적 식별)

  • Seok, Jongwon
    • Journal of Korea Multimedia Society
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    • v.19 no.10
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    • pp.1775-1781
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    • 2016
  • Generally, in the underwater target recognition, feature vectors are extracted from the target signal utilizing spatial information according to target shape/material characteristics. In addition, various signal processing techniques have been studied to extract feature vectors which are less sensitive to the location of the receiver. In this paper, we synthesized active echo signals using 3-dimensional highlight distribution. Then, Fractional Fourier transform was applied to echo signals to extract signal features. For the performance verification, classification experiments were performed using backpropagation and probabilistic neural network classifiers based on single aspect and multi-aspect method. As a result, we obtained a better recognition result using proposed feature extraction and multi-aspect based method.