This study devotes to uncertainty principles under the linear canonical transform (LCT) of a complex signal. A lowerbound 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.Index Terms-Complex signal, fractional Fourier transform, linear canonical transform (LCT), uncertainty principle.
In this paper, we obtain a necessary and sufficient condition for the incompleteness of complex exponential polynomials in C a ; where C a is a weighted Banach space of complex continuous functions f on the real axis R with f ðtÞ expðÀaðtÞÞ vanishing at infinity, in the uniform norm with respect to the weight aðtÞ: We also prove that, if the above condition of incompleteness holds, then each function in the closure of complex exponential polynomials can be extended to an entire function represented by a Dirichlet series. r
The Dirac-[Formula: see text] distribution may be realized through sequences of convolutions, the latter being also regarded as approximation to the identity. This paper proposes the real form of pre-orthogonal adaptive Fourier decomposition (POAFD) method to realize fast approximation to the identity. It belongs to sparse representation of signals having potential applications in signal and image analysis.
In the present paper, we introduce new subclasses of certain meromorphic multivalent functions defined by a class of linear operators involving the Liu-Srivastava operator, and investigate the majorization properties for functions belonging to these classes. Also, we point out some useful consequences of our main results.
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