Journal ArticleDOI
On the transform property of a band-limited function and its samples
A. Erteza,Kun-Shan Lin +1 more
- Vol. 68, Iss: 11, pp 1449-1450
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This correspondence introduces a new transform pair for any well behaved but arbitrary function f(t) and, thereafter, establishes two transform relationships between a band-limited function and its sample values.Abstract:
Sampling and reconstruction of band-limited functions are fundamental problems in communications and signal processing. This correspondence introduces a new transform pair for any well behaved but arbitrary function f(t) and, thereafter, establishes two transform relationships between a band-limited function and its sample values. This work can be viewed as yet another comment and extension on the sampling theorem.read more
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Book
Handbook of Fourier Analysis & Its Applications
TL;DR: In this article, Fourier Transforms in Probability, Random Variables and Stochastic Processes are used for time-frequency representation of signal and image synthesis in the context of Fourier analysis.
Journal ArticleDOI
Restoring causal signals by analytic continuation: A generalized sampling theorem for causal signals
TL;DR: In this article, a generalized sampling theorem for causal signals is derived; the total causal signal x(t) can be completely restored by sampling the band-limited part x 0 (t) with finite sampling frequency.
Journal ArticleDOI
Note on the transform property of band-limited functions
J.L. Brown,L.M. Roytman +1 more
TL;DR: In this paper, it was shown that the expansion theorem of the Erteza-Lin paper involves an incomplete set of orthogonal functions and consequently lacks the generality claimed for it.
References
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Journal ArticleDOI
XVIII.—On the Functions which are represented by the Expansions of the Interpolation-Theory
TL;DR: In this article, the authors consider a function of a variable x such that its Taylor expansion in any part of the plane of the complex variable x can be derived from its Taylor's expansion in another part by the process of analytic continuation.
Journal ArticleDOI
Error analysis in sampling theory
TL;DR: The most common sampling errors are round-off of f(nT), truncation of the series generating f(t), aliasing of frequency components above half the sampling rate 1/T, jitter in the recording times nT, loss of a number of sampled values, and imperfect filtering in the recovery of f (t).