Papoulis' sampling theorem: Revisited

Tantary, Azhar Y.; Shah, Firdous A.; Zayed, Ahmed I.

doi:10.1016/j.acha.2023.01.003

Cited by 5 publications

(1 citation statement)

References 23 publications

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“…It is imperative to mention that the classical GSE in the Fourier domain is a powerful ramification of the conventional Shannon's sampling theorem [22] which has found numerous applications in diverse aspects of signal and image processing, such as digital flight control, flexible analog-to-digital converters, data compression, image super-resolution and several other fields [23][24][25][26]. The GSE is often referred to as the multi-channel sampling expansion, mainly for the reason that it relies on non-uniform or multi-channel data acquisition [27,28,31]. The multi-channel sampling procedure allows the signal reconstruction at a decimated sampling rate determined by the number of channels used for the purpose of data acquisition.…”

Section: Moreover the Conjugate Of Any Quaternion H Is Given Bymentioning

confidence: 99%

Generalized sampling expansion for the quaternion linear canonical transform

Siddiqui,

Bing-Zhao,

Samad

2024

SIViP

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The theory of quaternions has gained firm ground in recent times and is being widely explored, with the field of signal and image processing being no exception. However, many important aspects of quaternionic signals are yet to be explored, particularly the formulation of Generalized Sampling Expansions (GSE). In the present article, our aim is to formulate the GSE in the realm of a one-dimensional quaternion linear canonical transform (QLCT). To facilitate the intent, we construct a set of quaternion-valued filter functions which are used to construct a system of equations determining the synthesis functions for the process of reconstruction. Besides, as a special case, another sampling formula involving the derivatives of the quaternionic signal is also obtained in the sequel. Since derivatives contain information about the edges and curves appearing in images, therefore, by invoking the higher degrees of freedom pertaining to QLCT, the obtained sampling formula can be used to develop new image scaling algorithms with state-of-the-art flexibility. As an endorsement of the obtained results, an example with simulations demonstrating the signal reconstruction is presented at the end.

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Section: Moreover the Conjugate Of Any Quaternion H Is Given Bymentioning

confidence: 99%

Generalized sampling expansion for the quaternion linear canonical transform

Siddiqui,

Bing-Zhao,

Samad

2024

SIViP

View full text Add to dashboard Cite

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Uncertainty principles for short‐time free metaplectic transformation

Zhang,

2024

Math Methods in App Sciences

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This study devotes to extend Heisenberg's uncertainty inequalities in free metaplectic transformation (FMT) domains into short‐time free metaplectic transformation (STFMT) domains. We disclose an equivalence relation between spreads in time‐STFMT and time domains, as well as FMT‐STFMT and FMT domains. We use them to set up an inequality relation between the uncertainty product in time‐STFMT and FMT‐STFMT domains and that in time and FMT domains and an inequality relation between the uncertainty product in two FMT‐STFMT domains and that in two FMT domains. We deduce uncertainty inequalities of real‐valued functions and complex‐valued window functions for the STFMT and uncertainty inequalities of complex‐valued (window) functions for the orthogonal STFMT, the orthonormal STFMT, and the STFMT without the assumption of orthogonality, respectively. To formulate the attainable lower bounds, we also propose some novel uncertainty inequalities of complex‐valued (window) functions for the orthogonal FMT and the FMT without the assumption of orthogonality, respectively.

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