Spectral Analysis and Reconstruction for Periodic Nonuniformly Sampled Signals in Fractional Fourier Domain

Tao, Ran; Li, Bing‐Zhao; Wang, Yue

doi:10.1109/tsp.2007.893931

Cited by 86 publications

(33 citation statements)

References 19 publications

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“…Step 8) The estimated output of can be obtained by selecting the median values of the real and the imaginary parts separately: (13) Step 9) By multiplying another chirp function to the estimation result obtained from the above steps, the output of the SDFrFT algorithm is finally given by (14) where is the sampling interval of the output signal, and is the length of the DFrFT output. The detailed overall computation architecture for the situation is presented in Fig.…”

Section: Methodsmentioning

confidence: 99%

“…In our previous related works, we investigated the spectral analysis and reconstruction in the fractional Fourier domain [13], the fractional power spectrum [14], the sampling theorems in the fractional Fourier domain [15], [16], time delay estimation of chirp signals in the fractional Fourier domain [17], and the short-time FrFT [18]. On this basis, we propose the sparse discrete fractional Fourier transform (SDFrFT) to achieve fast computation of DFrFT in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Sparse Discrete Fractional Fourier Transform and Its Applications

Liu¹,

Shan²,

Tao³

et al. 2014

IEEE Trans. Signal Process.

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134

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Abstract-The discrete fractional Fourier transform is a powerful signal processing tool with broad applications for nonstationary signals. In this paper, we propose a sparse discrete fractional Fourier transform (SDFrFT) algorithm to reduce the computational complexity when dealing with large data sets that are sparsely represented in the fractional Fourier domain. The proposed technique achieves multicomponent resolution in addition to its low computational complexity and robustness against noise. In addition, we apply the SDFrFT to the synchronization of high dynamic direct-sequence spread-spectrum signals. Furthermore, a sparse fractional cross ambiguity function (SFrCAF) is developed, and the application of SFrCAF to a passive coherent location system is presented. The experiment results confirm that the proposed approach can substantially reduce the computation complexity without degrading the precision.Index Terms-Cross ambiguity function, global positioning system, passive bistatic radar, sparse discrete fractional Fourier transform.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sparse Discrete Fractional Fourier Transform and Its Applications

Liu¹,

Shan²,

Tao³

et al. 2014

IEEE Trans. Signal Process.

Self Cite

134

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“…In many practical applications, we can utilize interleaving/multiplexing techniques to extend the capabilities of the monolithic A/D converters; due to the imperfect sampling timebase of interleaving/multiplexing techniques, the periodic nonuniformly sampling will be introduced. Since the chirp signals and radar signals are suitable for process in the fractional Fourier domain, we have explored the spectral properties of the periodic nonuniformly sampled signals in the fractional Fourier domain, including the general spectral representation of the periodic nonuniformly sampled signals and the fractional Fourier spectrum relationship between the sampled signal and the original signal [24] . In ref.…”

Section: Reconstruction For Periodic Nonuniform Samples Of the Fractimentioning

confidence: 99%

“…In ref. [24], the detailed analysis of periodic nonuniformly sampled chirp signals in the fractional Fourier domain has been also performed. Here, we present the interpolation expression for the periodic nonuniformly sampled signals by utilizing Theorem 1.…”

Section: Reconstruction For Periodic Nonuniform Samples Of the Fractimentioning

confidence: 99%

“…However, there are a variety of applications in which data is sampled with the band-limited signals in the fractional Fourier domain through multi-channel data acquisition, such as flexible interleaving/multiplexing analog-to-digital (A/D) converter for band-limited signal in the fractional Fourier domain (including chirp signal and other nonstationary signal) [24] , the orthogonal frequency division multiplexing (OFDM) system based on the FRFT for time-frequency selective channels, etc. [25,26] .…”

Section: Introductionmentioning

confidence: 99%

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Multi-channel sampling theorems for band-limited signals with fractional Fourier transform

Zhang

Tao

Wang

2008

Sci. China Ser. E-Technol. Sci.

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Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies.fractional Fourier transform, fractional band-limited signals, fractional filter, interpolation series, periodic nonuniformly sampled signal

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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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Spectral Analysis and Reconstruction for Periodic Nonuniformly Sampled Signals in Fractional Fourier Domain

Cited by 86 publications

References 19 publications

Sparse Discrete Fractional Fourier Transform and Its Applications

Sparse Discrete Fractional Fourier Transform and Its Applications

Multi-channel sampling theorems for band-limited signals with fractional Fourier transform

Convolution theorem for fractional cosine‐sine transform and its application

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