[波粒二象性，？，量子] 三张螺旋桨飞机飞行的照片

螺旋桨飞机： propeller aircraft

波粒二象性： wave-particle duality

采样定理： Whittaker-Kotel'nikov-Shannon sampling theorem, WKS-sampling theorem, WKS-theorem

一、三张螺旋桨飞机飞行的照片

图1  CICARE CH-14 Aguilucho (14-9904)

https://photos.flightaware.com/photos/retriever/1a87762a988fc340e40094c63b1a23caa3accf91

https://www.flightaware.com/photos/view/1352940-1c3ddad36d7e3171e01f69e2c056d0020a9b0808/staffpicksweek/sort/date/page/1

图2  Grumman G-44 Widgeon (C-FWVV)

https://photos.flightaware.com/photos/retriever/eaf76a2a306524b1d27c51490f47afff210f0ec3

 https://www.flightaware.com/photos/view/1352940-4088d8f02c26c5e37da538b1688bcb0dee51aa7e/staffpicksweek/sort/date/page/1

图3  Grumman G-36 Wildcat (N5HP)

 https://photos.flightaware.com/photos/retriever/a2bddeadc74fb398ef89a848fce932d88bf9a524

 https://www.flightaware.com/photos/view/10279523-5b6cae56ac4c9bbf3376b5f99c67ee1d0856b8fb/staffpicksweek/sort/date/page/1

二、采样定理（WKS-theorem）的发展时间节点

Whittaker-Kotel'nikov-Shannon (WKS) sampling theorem

   （1）1915年，E. T. Whittaker (Edmund Taylor Whittaker) 发表的统计理论。

   （2）采样定理是1928年由美国电信工程师 H.奈奎斯特 Nyquist (Harry Nyquist) 首先提出来的，因此称为奈奎斯特采样定理。

   （3）1933年由苏联工程师科捷利尼科夫 Kotelnikov 首次用公式严格地表述这一定理，因此在苏联文献中称为科捷利尼科夫采样定理。

   （4）1948年信息论的创始人 C.E.香农 (Claude Elwood Shannon) 对这一定理加以明确地说明并正式作为定理引用，因此在许多文献中又称为香农采样定理。（直到 1949 年，克劳德·香农才重新发现了采样定理。）

   由于 1915~1933年 Whittaker、Nyquist、Kotelnikov 的工作没有传播开来，才导致 1949 年 Shannon 重新发现了采样定理。

参考资料：

[1] 2022-01-20，波粒二象性/wave-particle duality/孙昌璞，中国大百科全书，第三版网络版[DB/OL]

https://www.zgbk.com/ecph/words?SiteID=1&ID=215481&Type=bkzyb&SubID=146659

[2] 2022-01-20，波粒二象性/wave-particle duality/董光璧，张一粟，中国大百科全书，第三版网络版[DB/OL]

https://www.zgbk.com/ecph/words?SiteID=1&ID=246958&Type=bkzyb&SubID=137861

[3] 2023-04-06，采样定理/sampling theorem/杨述明，中国大百科全书，第三版网络版[DB/OL]

https://www.zgbk.com/ecph/words?SiteID=1&ID=509900&Type=bkzyb&SubID=260688

[4] P. L. Butzer, P. J. S. G. Ferreira, J. R. Higgins, S. Saitoh, G. Schmeisser, R. L. Stens. Interpolation and Sampling: E.T. Whittaker, K. Ogura and Their Followers [J]. Journal of Fourier Analysis and Applications, 2011, 17(2): 320-354.

doi:  10.1007/s00041-010-9131-8

https://link.springer.com/article/10.1007/s00041-010-9131-8#Bib1  

[5] Harry Nyquist. Certain topics in telegraph transmission theory [J]. Transactions of the American Institute of Electrical Engineers, 1928, 47(2): 617 - 644.

doi: 10.1109/T-AIEE.1928.5055024

https://ieeexplore.ieee.org/document/5055024

https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5055024

[6] V A Kotel'nikov. On the transmission capacity of 'ether' and wire in electric communications [J]. Physics-Uspekhi, 2006, 49(7): 736-744.

doi:  10.1070/PU2006v049n07ABEH006160

https://iopscience.iop.org/article/10.1070/PU2006v049n07ABEH006160

https://iopscience.iop.org/article/10.1070/PU2006v049n07ABEH006160/pdf

[7] Neon A Armand. V A Kotel'nikov and his role in the development of radiophysics and radio engineering [J]. Physics-Uspekhi, 2006, 49(7): 744-748.

doi:  10.1070/PU2006v049n07ABEH006048

https://iopscience.iop.org/article/10.1070/PU2006v049n07ABEH006048

https://iopscience.iop.org/article/10.1070/PU2006v049n07ABEH006048/pdf

[8] Hans Dieter Lüke. The origins of the sampling theorem [J]. IEEE Communications Magazine, 1999, 37(4):  106 - 108.

doi:  10.1109/35.755459

https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=755459

https://ieeexplore.ieee.org/document/755459

[9] Chris Bissell. Vladimir Aleksandrovich Kotelnikov: pioneer of the sampling theorem, cryptography, optimal detection, planetary mapping [J]. IEEE Communications Magazine, 2009, 47(10): 24 - 32.

doi:  10.1109/MCOM.2009.5273804

https://ieeexplore.ieee.org/document/5273804

https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=5273804

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https://blog.sciencenet.cn/blog-107667-1359817.html

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https://blog.sciencenet.cn/blog-107667-1442847.html

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