Multichannel Consistent Sampling and Reconstruction Associated With Linear Canonical Transform

Xu, Liyun; Tao, Ran; Zhang, Feng

doi:10.1109/lsp.2017.2683535

Cited by 25 publications

(5 citation statements)

References 18 publications

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“…As a generalization of the FT and FRFT, the LCT equips three free parameters, and can be seen as an affine transformation in time‐frequency domain. Since the LCT's fast discrete algorithms were proposed [ 43‐57 ] , a large number of achievements have emerged in its mathematical foundations (convolution theorems [ 5 , 58‐64 ] , sampling theorems [ 60 , 61 , 65‐79 ] , uncertainty principles [ 80‐91 ] , etc. ), theoretical expansions (time‐frequency analysis [ 92‐99 ] , compressed sensing [ 100 ] , phase retrieval [ 101 ] , etc.…”

Section: Preliminariesmentioning

confidence: 99%

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

ZHANG

2022

Chinese J of Electronics

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By solving the existing expectation‐signal‐to‐noise ratio (expectation‐SNR) based inequality model of the closed‐form instantaneous cross‐correlation function type of Choi‐Williams distribution (CICFCWD), the linear canonical transform (LCT) free parameters selection strategies obtained are usually unsatisfactory. Since the second‐order moment variance outperforms the first‐order moment expectation in accurately characterizing output SNRs, this paper uses the variance analysis technique to improve parameters selection strategies. The CICFCWD's average variance of deterministic signals embedded in additive zero‐mean stationary circular Gaussian noise processes is first obtained. Then the so‐called variance‐SNRs are defined and applied to model a variance‐SNR based inequality. A stronger inequalities system is also formulated by integrating expectation‐SNR and variance‐SNR based inequality models. Finally, a direct application of the system in noisy one‐component and bi‐component linear frequency‐modulated (LFM) signals detection is studied. Analytical algebraic constraints on LCT free parameters newly derived seem more accurate than the existing ones, achieving better noise suppression effects. Our methods have potential applications in optical, radar, communication and medical signal processing.

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Section: Preliminariesmentioning

confidence: 99%

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

ZHANG

2022

Chinese J of Electronics

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“…The transformation can be the derivative, the Hilbert transform, or more general liner time invariant system [3]. The classical multichannel sampling theorem [1] is only available for the bandlimited functions in the sense of Fourier transform and it has been generalized for the bandlimited functions in the sense of fractional Fourier transform (FrFT) [4], linear canonical transform (LCT) [5,6] and offset LCT [7]. In a real application, only finitely many samples, albeit with large amount, are given in a bounded region [8].…”

Section: Introductionmentioning

confidence: 99%

Signal reconstruction from noisy multichannel samples

Chen¹,

Hu²,

Kou³

2022

Preprint

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We consider the signal reconstruction problem under the case of the signals sampled in the multichannel way and with the presence of noise. Observing that if the samples are inexact, the rigorous enforcement of multichannel interpolation is inappropriate. Thus the reasonable smoothing and regularized corrections are indispensable. In this paper, we propose several alternative methods for the signal reconstruction from the noisy multichannel samples under different smoothing and regularization principles. We compare these signal reconstruction methods theoretically and experimentally in the various situations. To demonstrate the effectiveness of the proposed methods, the probability interpretation and the error analysis for these methods are provided. Additionally, the numerical simulations as well as some guidelines to use the methods are also presented.

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“…Signal sampling is a fundamental concept in digital signal processing, as it provides a bridge between continuous-and discrete-time signals. A variety of sampling theorems in the traditional FT domain have been generalized to the LCT domain in the broad sense that signals which are non-bandlimited in the FT domain may be bandlimited in the LCT domain [12][13][14][15][16][17][18]. In recent years, dynamical sampling has attracted empirical attention in the scientific community, which is a new way of signal sampling, compared with classical sampling techniques, and has potential applications to wireless sensor networks in the health, environment, and precision agriculture industries [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Multivariate Dynamical Sampling in $l^2(\mathbb{Z}^2)$ and Shift-Invariant Spaces Associated with Linear Canonical Transform

Huo¹,

Xiao²

2021

Preprint

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In this paper, we investigate the multivariate dynamical sampling problem in l 2 (Z 2 ) associated with the two-dimensional discrete time non-separable linear canonical transform (2D-DT-NS-LCT) and shift-invariant spaces associated with the two-dimensional non-separable linear canonical transform (2D-NS-LCT), respectively. Specifically, we derive a sufficient and necessary condition under which a sequence in l 2 (Z 2 ) (or a function in a shift-invariant space) can be stably recovered from its dynamical sampling measurements associated with the 2D-DT-NS-LCT (or the 2D-NS-LCT). We also present a simple example to elucidate our main results.

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Multichannel Consistent Sampling and Reconstruction Associated With Linear Canonical Transform

Cited by 25 publications

References 18 publications

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

Variance‐SNR Based Noise Suppression on Linear Canonical Choi‐Williams Distribution of LFM Signals

Signal reconstruction from noisy multichannel samples

Multivariate Dynamical Sampling in $l^2(\mathbb{Z}^2)$ and Shift-Invariant Spaces Associated with Linear Canonical Transform

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