Uncertainty principles for linear canonical transform.
ABSTRACT This correspondence investigates the uncertainty principles under the linear canonical transform (LCT). First, a lower bound on the uncertainty product of signal representations in two LCT domains for complex signals is derived, which can be achieved by a complex chirp signal with Gaussian envelope. Then, the tighter lower bound for real signals in two LCT domains proposed by Sharma and Joshi is also proven to hold for arbitrary LCT parameters based on the properties of moments for the LCT. The uncertainty principle for the fractional Fourier transform is a special case of the achieved results.
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ABSTRACT: Academic Editor: Zhan Shu Copyright q 2012 B.-Z. Li and T.-Z. Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The spectral analysis of uniform or nonuniform sampling signal is one of the hot topics in digital signal processing community. Theories and applications of uniformly and nonuniformly sampled one-dimensional or two-dimensional signals in the traditional Fourier domain have been well studied. But so far, none of the research papers focusing on the spectral analysis of sampled signals in the linear canonical transform domain have been published. In this paper, we investigate the spectrum of sampled signals in the linear canonical transform domain. Firstly, based on the properties of the spectrum of uniformly sampled signals, the uniform sampling theorem of two dimensional signals has been derived. Secondly, the general spectral representation of periodic nonuniformly sampled one and two dimensional signals has been obtained. Thirdly, detailed analysis of periodic nonuniformly sampled chirp signals in the linear canonical transform domain has been performed.Mathematical Problems in Engineering 01/2012; 2012. · 1.38 Impact Factor
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ABSTRACT: The linear canonical transform (LCT) has proven to be a powerful tool in optics and signal processing. Most existing sampling theories of this transform were derived from the LCT band-limited signal viewpoint. However, in the real world, many analog signals encountered in practical engineering applications are non-bandlimited. The purpose of this paper is to derive sampling theorems of the LCT in function spaces for frames without band-limiting constraints. We extend the notion of shift-invariant spaces to the LCT domain and then derive a sampling theorem of the LCT for regular sampling in function spaces with frames. Further, the theorem is modified to the shift sampling in function spaces by using the Zak transform. Sampling and reconstructing signals associated with the LCT are also discussed in the case of Riesz bases. Moreover, some examples and applications of the derived theory are presented. The validity of the theoretical derivations is demonstrated via simulations.Signal Processing 05/2014; 98:88 - 95. · 2.24 Impact Factor
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ABSTRACT: This study devotes to uncertainty principles under the linear canonical transform (LCT) of a complex signal. A lower-bound for the uncertainty product of a signal in the two LCT domains is proposed that is sharper than those in the existing literature. We also deduce the conditions that give rise to the equal relation of the new uncertainty principle. The uncertainty principle for the fractional Fourier transform is a particular case of the general result for LCT. Examples, including simulations, are provided to show that the new uncertainty principle is truly sharper than the latest one in the literature, and illustrate when the new and old lower bounds are the same and when different.IEEE Transactions on Signal Processing 11/2013; 61(21):5153-5164. · 2.81 Impact Factor