Whittaker–Kotelnikov–Shannon Sampling Theorem and Aliasing Error

Gensun, Fang

doi:10.1006/jath.1996.0033

Cited by 60 publications

(13 citation statements)

References 11 publications

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“…The result (1) turns out to be a variant of the L p version of the sampling theorem, which has been given by Gensun [4]. We shall give a simpler proof than his.…”

Section: Definition 24mentioning

confidence: 84%

“…To prove these results, the L p version of the sampling theorem is used. Its elementary proof will be given and the unconditionality of the convergence of (1.2), which was not stated explicitly in [4], will be shown.…”

Section: Introductionmentioning

confidence: 99%

“…We say that a function ( The classical sampling theorem has been generalized in various directions. One such generalization given by Gensun [4] extends the function space, which contains bandlimited functions, from L 2 ðRÞ to L p ðRÞ, 1 < p < 1.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet Bases for Microlocal Filtering and the Sampling Theorem inL_p(Rⁿ)∗

Ashino

Mandai

2003

Applicable Analysis

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An orthonormal wavelet basis in L 2 ðR n Þ used for microlocal filters, which decompose signals into microlocal contents, is shown to be a ''stepwise'' unconditional basis in L p ðR n Þ (1 < p < 1). Other related spaces are also treated. As part of the proof, an elementary proof of the L p version of the sampling theorem with unconditional convergence is given. Finally, an application is given to the expression of some distributions as sums of boundary values of holomorphic functions.

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“…The result (1) turns out to be a variant of the L p version of the sampling theorem, which has been given by Gensun [4]. We shall give a simpler proof than his.…”

Section: Definition 24mentioning

confidence: 84%

Section: Introductionmentioning

confidence: 99%

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Wavelet Bases for Microlocal Filtering and the Sampling Theorem inL_p(Rⁿ)∗

Ashino

Mandai

2003

Applicable Analysis

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“…In the several decades since both Shannon [129] and Nyquist [130], there has been considerable development in understanding of sampling theory [129][130][131][132][133][134][135][136][137][138][139][140][141][142][143][144]. Shannon's theorem shows how appropriate band-limiting allows repeated resampling of a signal without build-up of alias products.…”

Section: Samplingmentioning

confidence: 99%

“…With rectangular sampling the noise is finite but still with a significant contribution from downward-aliased components. Triangular (spline order 2) sampling reduces this contribution to insignificance given a white noise spectrum, however a rising input noise spectrum may suggest using a spline of order 3 or higher [134,135,[139][140][141][142].…”

Section: Sampling Spline Ordermentioning

confidence: 99%

A Hierarchical Approach for Audio Capture, Archive, and Distribution

Stuart¹,

Craven²

2019

J. Audio Eng. Soc.

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Recent interest in high-resolution digital audio has been accompanied by a trend to higher and higher sampling rates and bit depths, yet the sound quality improvements show diminishing returns and so fail to reconcile human auditory capability with the information capacity of the channel. We propose an audio capture, archiving, and distribution methodology based on sampling kernels having finite length, unlike the "ideal" sinc kernel that extends indefinitely. We show that with the new kernels, original transient events need not become significantly extended in time when reproduced. This new approach runs contrary to some conventional audio desiderata such as the complete elimination of aliasing. The paper reviews advances in neuroscience and recent evidence on the statistics of real signals, from which we conclude that the conventional criteria may be unhelpful. We show that this proposed approach can result in improved time/frequency balance in a high-performance chain whose errors, from the perspective of the human listener, are equivalent to those introduced when sound travels a short distance through air.

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