Fractional convolution and correlation via operator methods and an application to detection of linear FM signals

Akay, Olcay; Boudreaux-Bartels, G.F.

doi:10.1109/78.917802

Cited by 146 publications

(108 citation statements)

References 31 publications

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“…In addition, 1000 trial runs have been performed for each assessment. It is clear from (11) and (14) that the performance of the proposed scheme depends on the selection of appropriate values of the angle parameters 1 and 2 in the design of the TS. For the performance assessment, we have selected 1 = − 2 .…”

Section: Simulation Setup and Resultsmentioning

confidence: 99%

“…For each value of ϕ, the th-order FRFT rotates a time-domain signal counterclockwise by ϕ [11]. In general, we can relate ϕ and α as follows [10]:…”

Section: Operation Principlementioning

confidence: 99%

“…To detect chirp signal 1, for each block, we define a detection metric 1 ( ), obtained from the fractional cross-correlation [11] of the block with the original transmitted chirp signal 1 as follows:…”

Section: B Joint Frame and Frequency Synchronizationmentioning

confidence: 99%

See 2 more Smart Citations

Discrete FRFT-Based Frame and Frequency Synchronization for Coherent Optical Systems

Omomukuyo¹,

Zhang²,

Dobre³

et al. 2017

IEEE Photon. Technol. Lett.

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Chirp signals are used to construct a training sequence (TS), and fractional cross-correlation is employed to define a detection metric for the TS, from which a set of equations can be obtained. Estimates of both the timing offset and carrier frequency offset (CFO) are obtained by solving these equations. This TS is later employed in a phase-dependent decision-directed least-mean square algorithm for adaptive equalization. Simulation results of a 32-Gbaud coherent polarization division multiplexed Nyquist system show that the proposed scheme has a wide CFO estimation range and accurate synchronization performance even in poor optical signal-to-noise ratio conditions.

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Section: Simulation Setup and Resultsmentioning

confidence: 99%

“…For each value of ϕ, the th-order FRFT rotates a time-domain signal counterclockwise by ϕ [11]. In general, we can relate ϕ and α as follows [10]:…”

Section: Operation Principlementioning

confidence: 99%

See 1 more Smart Citation

Discrete FRFT-Based Frame and Frequency Synchronization for Coherent Optical Systems

Omomukuyo¹,

Zhang²,

Dobre³

et al. 2017

IEEE Photon. Technol. Lett.

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show abstract

“…The cross-fractional correlation function can be used to describe the relation between two functions or sequences [26]. Therefore it can be used to find differences between the fault-free case and the faulty case of the CUT or between two faulty cases.…”

mentioning

confidence: 99%

“…The mth element of B is B(m). According to reference [26], the cross-fractional correlation function between two continuous-time functions 1 () ft and 2 () ft is…”

mentioning

confidence: 99%

Diagnosis of Incipient Faults in Nonlinear Analog Circuits

Deng¹,

Shi²,

Zhang³

2012

Metrology and Measurement Systems

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Considering the problem to diagnose incipient faults in nonlinear analog circuits, a novel approach based on fractional correlation is proposed and the application of the subband Volterra series is used in this paper. Firstly, the subband Volterra series is calculated from the input and output sequences of the circuit under test (CUT). Then the fractional correlation functions between the fault-free case and the incipient faulty cases of the CUT are derived. Using the feature vectors extracted from the fractional correlation functions, the hidden Markov model (HMM) is trained. Finally, the well-trained HMM is used to accomplish the incipient fault diagnosis. The simulations illustrate the proposed method and show its effectiveness in the incipient fault recognition capability.

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Convolution theorem for fractional cosine‐sine transform and its application

Feng

2016

Math Methods in App Sciences

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Fractional cosine transform (FRCT) and fractional sine transform (FRST), which are closely related to the fractional Fourier transform (FRFT), are useful mathematical and optical tool for signal processing. Many properties for these transforms are well investigated, but the convolution theorems are still to be determined. In this paper, we derive convolution theorems for the fractional cosine transform (FRCT) and fractional sine transform (FRST) based on the four novel convolution operations. And then, a potential application for these two transforms on designing multiplicative filter is presented. Copyright © 2016 John Wiley & Sons, Ltd.

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Fractional convolution and correlation via operator methods and an application to detection of linear FM signals

Cited by 146 publications

References 31 publications

Discrete FRFT-Based Frame and Frequency Synchronization for Coherent Optical Systems

Discrete FRFT-Based Frame and Frequency Synchronization for Coherent Optical Systems

Diagnosis of Incipient Faults in Nonlinear Analog Circuits

Convolution theorem for fractional cosine‐sine transform and its application

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