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. 2020 May 18;11:2479. doi: 10.1038/s41467-020-16262-0

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© The Author(s) 2020

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.

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Fig. 1 — This figure shows the relationship between sampling, PAM and PWM. Both time-domain waveforms and frequency-domain spectrum are depicted. a The continuous original signal to be sampled or modulated. b An impulse train, which is a sequence of Dirac functions and can be employed as a sampling function. c The ideal sampling result, which is the result of the multiplication of a and b in the time domain and convolution in the frequency domain. d A pulse in the time domain and its corresponding spectrum. e The sampling result obtained in practice, in which case the periodic sequence of impulses (Dirac functions) is replaced with a sequence of pulses of equal width. This process is also known as PAM. This result is derived through the convolution of c and d in the time domain and multiplication in the frequency domain. f The result of PWM—derived from e in the time domain based on the area equivalence principle.