Some general aspects of the sampling theorem

Jagerman, David L.; Fogel, Lawrence J.

doi:10.1109/tit.1956.1056821

Cited by 97 publications

(57 citation statements)

References 4 publications

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“…3(a) and (b), where (4) Note that (4) implies that , where is the discrete-time impulse response with frequency response , and is the continuous-time impulse response with frequency response . Since , the sequence is, in general, an undersampled representation of , and consequently, is, in general, a filtered and aliased version of .…”

Section: Interpolation Identitymentioning

confidence: 99%

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Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples

Eldar

Oppenheim

2000

IEEE Trans. Signal Process.

175

122

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Abstract-This paper introduces a filterbank interpretation of various sampling strategies, which leads to efficient interpolation and reconstruction methods. An identity, which is referred to as the Interpolation Identity, is developed and is used to obtain particularly efficient discrete-time systems for interpolation of generalized samples as well as a class of nonuniform samples, to uniform Nyquist samples, either for further processing in that form or for conversion to continuous time. The Interpolation Identity also leads to new sampling strategies including an extension of Papoulis' generalized sampling expansion.

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Section: Interpolation Identitymentioning

confidence: 99%

“…It is well known that a bandlimited signal can be reconstructed from uniform samples of the signal and its derivative at half the Nyquist rate [4] using the reconstruction formula sinc (5) where , and . Note that the sequences and are undersampled representations of and , respectively.…”

Section: Interpolation and Reconstruction From Samples Of A Signmentioning

confidence: 99%

Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples

Eldar

Oppenheim

2000

IEEE Trans. Signal Process.

175

122

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“…can be reconstructed from samples of amplitude and first derivative every 2T Nyq seconds [36,37] which leads to the study of this thesis. As illustrated in Fig.…”

Section: Bmentioning

confidence: 99%

Bandlimited Optical Intensity Modulation Under Average and Peak Power Constraints

Zhang

Hranilovic

2016

IEEE Trans. Commun.

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Bandlimited optical intensity channels, arising in applications such as indoor infrared communications and visible light communications (VLC), require that all signals satisfy a bandwidth constraint as well as average, peak and non-negative amplitude constraints. However, the signaling designed for conventional radio frequency (RF) electrical channels cannot be applied directly, since they take energy constraints into consideration instead of amplitude constraints. In addition, conventional transmission techniques optimized for broad-band optical channels such as fiber optics, terrestrial/satellite-to-satellite free-space optical (FSO) communications are typically not bandwidth efficient.In this thesis, a two-dimensional signal space for bandlimited optical intensity channels is presented. A novel feature of this model is that the non-negativity and peak amplitude constraints are relaxed. The signal space parameterizes the likelihood of a negative or peak amplitude excursions in the output. Although the intensity channel only supports non-negative amplitudes, the impact of clipping on system performance is shown to be negligible if the likelihood of negative amplitude excursion is small enough. For a given signal space, a tractable approximation approach using a finite series is applied to accurately compute the likelihood of clipping under average and peak optical power constraints. The uncoded asymptotic optical power and iv spectral efficiencies using two-dimensional lattice constellations are computed. The Monte-Carlo (MC) simulation results show that for a given average or peak optical power, schemes designed in the presented signal space haver higher spectral efficiency than M -ary pulse amplitude modulation (PAM) using previously established tech- g 1 (t) first branch receive filterg 2 (t) second branch receive filterh(t) channel response I(t) instantaneous optical intensity n(t) channel noise n 1,i output sample noise after filter g 1 (t) at i-th symbol interval n 2,i output sample noise after filter g 2 (t) at i-th symbol interval n c,1,i clipping distortion after filter g 1 (t) at i-th symbol interval n c,2,i clipping distortion after filter g 2 (t) at i-th symbol interval q variable defined as the ratio of t to symbol period T Q(·) tail probability of the standard normal distribution R residual sum r 1 (t) output waveform of filter g 1 (t)

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“…Note that Jagerman-Fogel [37] already applied such an approach in 1956 under somewhat different conditions.…”

Section: Theorem 1 the Cardinal Function Can Be Constructed Analyticamentioning

confidence: 99%

Interpolation and Sampling: E.T. Whittaker, K. Ogura and Their Followers

Butzer

Ferreira

Higgins³

et al. 2010

J Fourier Anal Appl

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The classical sampling theorem has often been attributed to E.T. Whittaker, but this attribution is not strictly valid. One must carefully distinguish, for example, between the concepts of sampling and of interpolation, and we find that Whittaker worked in interpolation theory, not sampling theory. Again, it has been said that K. Ogura was the first to give a properly rigorous proof of the sampling theorem. We find that he only indicated where the method of proof could be found; we identify what is, in all probability, the proof he had in mind. Ogura states his sampling theIn Memory of Gen-ichirô Sunouchi (1911-2008, a Great Mathematician and Human Being Communicated by Hans G. Feichtinger. P.L. Butzer · R.L. Stens ( ) Lehrstuhl

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Some general aspects of the sampling theorem

Cited by 97 publications

References 4 publications

Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples

Filterbank reconstruction of bandlimited signals from nonuniform and generalized samples

Bandlimited Optical Intensity Modulation Under Average and Peak Power Constraints

Interpolation and Sampling: E.T. Whittaker, K. Ogura and Their Followers

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