Reconstruction of Uniformly Sampled Sequence From Nonuniformly Sampled Transient Sequence Using Symmetric Extension

Park, Sung-Won; Hao, Wei-Da; Leung, Chung S.

doi:10.1109/tsp.2011.2177834

Cited by 11 publications

(8 citation statements)

References 10 publications

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“…Finally, we can reconstruct the uniformly sampled sequence by taking the inverse transform of the obtained DFRFT F α [m]. It is easy to show that the result of (16) reduces to the result of [23] in the Fourier domain when α = π/2.…”

Section: Relationship Between Uniform Samples and Non-uniform Samplesmentioning

confidence: 99%

See 1 more Smart Citation

Reconstruction of uniformly sampled signals from non‐uniform short samples in fractional Fourier domain

Yang

Zhang

et al. 2016

IET signal process.

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Signal reconstruction from non-uniform samples, especially for non-stationary signals, is an important issue in the area of digital signal processing. As a type of signal processing tool, the fractional Fourier transform has been proved to be effective for solving problems in non-stationary signal processing. For non-stationary discrete-time signals, the reconstruction of uniformly sampled signals from non-uniform samples in the fractional Fourier domain is first derived in this study. Since only finite non-uniform samples are collected in practical applications, for preferable reconstruction, two types of symmetric extensions are considered in the reconstruction to overcome the discontinuity problem that exists in the periodisation of short non-stationary sequences, which is more critical than that of long sequences. In addition, the average signal-to-noise ratio is used to evaluate the performance of the reconstruction with two types of symmetric extensions. Simulations and two applications are given to verify the effectiveness of the proposed reconstruction method.

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Section: Relationship Between Uniform Samples and Non-uniform Samplesmentioning

confidence: 99%

“…In(23), f [n] is the ideal uniformly sampled sequence, andf [n] is the reconstructed uniformly sampled sequence by taking the inverse transform of F…”

mentioning

confidence: 99%

Reconstruction of uniformly sampled signals from non‐uniform short samples in fractional Fourier domain

Yang

Zhang

et al. 2016

IET signal process.

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“…Figure 6 demonstrates the relation between and * , and it is observed that the deviation * converges to 0.2942 when decreases to 0. In the following, our proposed method is compared with traditional methods, including CRT, Staggered PRF, and nonuniform sample [18], and the comparison results are presented in Table 2. Seen from Table 2, our proposed method transmits the least transmitting pulses.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Doppler Ambiguity Resolution Based on Random Sparse Probing Pulses

Zhang

Deng

Shi

et al. 2015

Journal of Electrical and Computer Engineering

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A novel method for solving Doppler ambiguous problem based on compressed sensing (CS) theory is proposed in this paper. A pulse train with the random and sparse transmitting time is transmitted. The received signals after matched filtering can be viewed as randomly sparse sampling from the traditional fixed-pulse repetition frequency (PRF) echo signals. The whole target echo could be reconstructed via CS recovery algorithms. Through refining the sensing matrix, which is equivalent to increase the sampling frequency of target characteristic, the Doppler unambiguous range is enlarged. In particular, Complex Approximate Message Passing (CAMP) algorithm is developed to estimate the unambiguity Doppler frequency. Cramer-Rao lower bound expressions are derived for the frequency. Numerical simulations validate the effectiveness of the proposed method. Finally, compared with traditional methods, the proposed method only requires transmitting a few sparse probing pulses to achieve a larger Doppler frequency unambiguous range and can also reduce the consumption of the radar time resources.

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“…These sampling theorems establish the fact that a bandlimited or timelimited signal in the LCT domain can be completely reconstructed by a set of equidistantly spaced signal samples [26][27][28][29][30][31][32][33][34][35][36][37][38]. However, there are a variety of applications in which the data are sampled in other ways, such as non-uniformly in time or through multichannel data acquisition [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]. Examples in which non-uniform sampling may arise include data loss because of channel erasures and additive noise [39,41,49].…”

Section: Introductionmentioning

confidence: 99%

“…There are also applications where we can benefit from deliberately introducing more elaborate sampling schemes. Potential applications include flexible A/D converters, the orthogonal frequency division multiplexing system, data compression and image super-resolution [10,11,43,[54][55][56][57][58][59][60][61]. Therefore it is theoretically interesting and practically useful to consider the multichannel sampling expansion in the LCT domain.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain

Wei

2014

IET signal process.

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The linear canonical transform (LCT) has been shown to be a powerful tool for optics and signal processing. In this study, the authors address the problem of signal reconstruction from the multidimensional multichannel samples in the LCT domain. Firstly, they pose and solve the problem of expressing the kernel of the multidimensional LCT in the elementary functions. Then, they propose the multidimensional multichannel sampling (MMS) for the bandlimited signal in the LCT domain based on a basis expansion of an exponential function. The MMS expansion which is constructed by the ordinary convolution structure can reduce the effect of the spectral leakage and is easy to implement. Thirdly, based on the MMS expansion, they obtain the reconstruction method for the multidimensional derivative sampling and the periodic non-uniform sampling by designing the system filter transfer functions. Finally, the simulation results and the potential applications of the MMS are presented. Especially, the application of the multidimensional derivative sampling in the context of the image scaling about the image super-resolution is discussed.

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Reconstruction of Uniformly Sampled Sequence From Nonuniformly Sampled Transient Sequence Using Symmetric Extension

Cited by 11 publications

References 10 publications

Reconstruction of uniformly sampled signals from non‐uniform short samples in fractional Fourier domain

Reconstruction of uniformly sampled signals from non‐uniform short samples in fractional Fourier domain

Doppler Ambiguity Resolution Based on Random Sparse Probing Pulses

Reconstruction of multidimensional bandlimited signals from multichannel samples in linear canonical transform domain

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