On n-dimensional sampling theorems

Chen, K. H.; Yang, Chunde

doi:10.1016/0096-3003(80)90047-8

Cited by 6 publications

(2 citation statements)

References 13 publications

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“…The spectrum of the sampling function is well known to be simply a periodic delta function separated by intervals equal to the sampling frequency. This behaviour is readily confirmed to be the case for the present work by substituting r ( u [ l ] ) = 1 and u [ l ] = l/N into equation (7). Comparing this behaviour with the definition of PIBL in Section 4.2 confirms that uniform sampling with constant weights exhibits PIBL.…”

Section: Uniform Weightssupporting

confidence: 67%

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An extension of Nyquist's theorem to non‐uniformly sampled finite length data

Belmont

1995

Adaptive Control & Signal

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This paper examines non-uniformly sampled functions on a finite interval. The aim is to investigate what conditions must be satisfied in order to recover the baseband spectrum from such data. It is shown that the concept of band limitation inherent in Nyquist's theorem must be generalized into a quantity termed primary interval bandwidth limitation. This property is explored and various algorithms are developed, including an extension of the classical band-limited interpolation formula. Measures are obtained that provide guidelines for assessing where approximate techniques can be employed and the use of these in adaptive scenarios is considered. The key results are illustrated by a set of numerical examples. The findings are presented in the context of time variables, but the approach is applicable to any type of sample domain. The treatment is one-dimensional, as are the examples discussed, but the extension to multiple dimensions is immediate and straightforward.

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Section: Uniform Weightssupporting

confidence: 67%

“…This is because equation (7) shows that the R-spectrum is a set of samples taken 2 n / T apart in the frequency domain from an almost periodic function. Only for the very special circumstances of uniform sampling are long sequences of samples in the primary interval equal to zero as required for PIBL.…”

Section: Uniform Weightsmentioning

confidence: 99%