The Algebraical Superposition Technic for Transformation from S Domain to Time Domain

Benqing Gao

doi:doi:10.11648/j.ajmp.20200904.11

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The Algebraical Superposition Technic for Transformation from S Domain to Time Domain

Benqing Gao

Published in American Journal of Modern Physics (Volume 9, Issue 4)

Received: 9 June 2020 Accepted: 7 July 2020 Published: 17 August 2020

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Abstract

An algebraical superposition technic for transformation from frequency domain to time domain is presented. The establishing model process are; From the inverse Laplace transform integral formula, the integral formula can be expressed by the series with k [-K, K] term., based on integral function distribution properties along integral path, the bidirectional series sum on k [-K, K] term series can be expressed by a monomial trigonomial function series sum on k [0, K]. In the paper the solution process and main points are presented. The application examples are shown; the results are supported to the algebraical superposition technic. In using above algebraical superposition technic to analysis airspace dispersive propagation poperties, i.e., to find out its time-domain parameters, the resultant formula contain time-domain factor and frequency-domain factor, that is first time to present in the paper, so it is called ‚’time-frequency union technic‘. In the paper simultaneity solve out wave number and wave impendance for waveguide TE10 mode propagation, and get both time-frequency union values, and show the soving process and soving accuracy.

Published in	American Journal of Modern Physics (Volume 9, Issue 4)
DOI	10.11648/j.ajmp.20200904.11
Page(s)	55-59
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Frequency Domain to Time Domain Trasformation, Laplace Transformation, Algebraical Superposition Technic, Rectangular Wavwguide TE10 Mode, Time-frequency Union Value

References

[1]	Zheng Jun li, Signal and system introduction, Beijing, High education publisher, 2009, p 420-438.
[2]	Wu xiang qi, Signal and system (third), Beijing, Electronic industry publisher, 2009, p 338.
[3]	Zeng Yu Cun deng, Signal and system (third), Beijing, Beijing Institute of Technology publisher, 2010, p. 266-283.
[4]	(USA) R. E. Collin, Translation: Chinese, Hou Yuanqing, Field theory of guided waves, Shanghai Science-technic Publisher, 1960, p 182-184.
[5]	Lu Shanwei, Microwave Engineering Foundation, Beijing aviation and spaceflight university publisher, 1995, P. 128-139.
[6]	Yan Yun Qing, Li Ying Hui, Micriwave Technic Fondamention (fourth), Beijing Instituteof Technology Publisher, 2011, P. 68-96.
[7]	Liang Kun Miao, Mathematic Physic Method, Beijing Education Publisher, 1978, p. 85-99.
[8]	Fu Dan University Mathematic Depatment Editor, Mathematic PhysicEquation (second), ShanghaiScience Technic Publisher, 1961, p. 78-94.
[9]	Mathematic handbook writing group, Mathematic handbook, Beijing, Pepole education publish, 1979, p. 553-564.
[10]	Po Go Neng, Fortran 95 Program Design, Beijinb, China electric power publisher, 2006, p. 562-567.
[11]	Ben-Qing Gao, An algebraical superposition technic for transformation from Z domain to time domain, 2018, WJRR, Vol. 6, May, P. 4-7.
[12]	Ben-Qing Gao, A new priciple technic for the transformation from frequency to time domain, 2017, AIP Advances 7, 035315, USA..

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Benqing Gao. (2020). The Algebraical Superposition Technic for Transformation from S Domain to Time Domain. American Journal of Modern Physics, 9(4), 55-59. https://doi.org/10.11648/j.ajmp.20200904.11

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Benqing Gao. The Algebraical Superposition Technic for Transformation from S Domain to Time Domain. Am. J. Mod. Phys. 2020, 9(4), 55-59. doi: 10.11648/j.ajmp.20200904.11

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AMA Style

Benqing Gao. The Algebraical Superposition Technic for Transformation from S Domain to Time Domain. Am J Mod Phys. 2020;9(4):55-59. doi: 10.11648/j.ajmp.20200904.11

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@article{10.11648/j.ajmp.20200904.11,
  author = {Benqing Gao},
  title = {The Algebraical Superposition Technic for Transformation from S Domain to Time Domain},
  journal = {American Journal of Modern Physics},
  volume = {9},
  number = {4},
  pages = {55-59},
  doi = {10.11648/j.ajmp.20200904.11},
  url = {https://doi.org/10.11648/j.ajmp.20200904.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20200904.11},
  abstract = {An algebraical superposition technic for transformation from frequency domain to time domain is presented. The establishing model process are; From the inverse Laplace transform integral formula, the integral formula can be expressed by the series with k [-K, K] term., based on integral function distribution properties along integral path, the bidirectional series sum on k [-K, K] term series can be expressed by a monomial trigonomial function series sum on k [0, K]. In the paper the solution process and main points are presented. The application examples are shown; the results are supported to the algebraical superposition technic. In using above algebraical superposition technic to analysis airspace dispersive propagation poperties, i.e., to find out its time-domain parameters, the resultant formula contain time-domain factor and frequency-domain factor, that is first time to present in the paper, so it is called ‚’time-frequency union technic‘. In the paper simultaneity solve out wave number and wave impendance for waveguide TE10 mode propagation, and get both time-frequency union values, and show the soving process and soving accuracy.},
 year = {2020}
}

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TY  - JOUR
T1  - The Algebraical Superposition Technic for Transformation from S Domain to Time Domain
AU  - Benqing Gao
Y1  - 2020/08/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ajmp.20200904.11
DO  - 10.11648/j.ajmp.20200904.11
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 55
EP  - 59
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20200904.11
AB  - An algebraical superposition technic for transformation from frequency domain to time domain is presented. The establishing model process are; From the inverse Laplace transform integral formula, the integral formula can be expressed by the series with k [-K, K] term., based on integral function distribution properties along integral path, the bidirectional series sum on k [-K, K] term series can be expressed by a monomial trigonomial function series sum on k [0, K]. In the paper the solution process and main points are presented. The application examples are shown; the results are supported to the algebraical superposition technic. In using above algebraical superposition technic to analysis airspace dispersive propagation poperties, i.e., to find out its time-domain parameters, the resultant formula contain time-domain factor and frequency-domain factor, that is first time to present in the paper, so it is called ‚’time-frequency union technic‘. In the paper simultaneity solve out wave number and wave impendance for waveguide TE10 mode propagation, and get both time-frequency union values, and show the soving process and soving accuracy.
VL  - 9
IS  - 4
ER  -

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Author Information

Benqing Gao

Beijing Institute of Technology, School of Information Science and Technology, Beijing, China

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Plain Text BibTeX RIS

APA Style

Benqing Gao. (2020). The Algebraical Superposition Technic for Transformation from S Domain to Time Domain. American Journal of Modern Physics, 9(4), 55-59. https://doi.org/10.11648/j.ajmp.20200904.11

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ACS Style

Benqing Gao. The Algebraical Superposition Technic for Transformation from S Domain to Time Domain. Am. J. Mod. Phys. 2020, 9(4), 55-59. doi: 10.11648/j.ajmp.20200904.11

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AMA Style

Benqing Gao. The Algebraical Superposition Technic for Transformation from S Domain to Time Domain. Am J Mod Phys. 2020;9(4):55-59. doi: 10.11648/j.ajmp.20200904.11

Copy | Download

@article{10.11648/j.ajmp.20200904.11,
  author = {Benqing Gao},
  title = {The Algebraical Superposition Technic for Transformation from S Domain to Time Domain},
  journal = {American Journal of Modern Physics},
  volume = {9},
  number = {4},
  pages = {55-59},
  doi = {10.11648/j.ajmp.20200904.11},
  url = {https://doi.org/10.11648/j.ajmp.20200904.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20200904.11},
  abstract = {An algebraical superposition technic for transformation from frequency domain to time domain is presented. The establishing model process are; From the inverse Laplace transform integral formula, the integral formula can be expressed by the series with k [-K, K] term., based on integral function distribution properties along integral path, the bidirectional series sum on k [-K, K] term series can be expressed by a monomial trigonomial function series sum on k [0, K]. In the paper the solution process and main points are presented. The application examples are shown; the results are supported to the algebraical superposition technic. In using above algebraical superposition technic to analysis airspace dispersive propagation poperties, i.e., to find out its time-domain parameters, the resultant formula contain time-domain factor and frequency-domain factor, that is first time to present in the paper, so it is called ‚’time-frequency union technic‘. In the paper simultaneity solve out wave number and wave impendance for waveguide TE10 mode propagation, and get both time-frequency union values, and show the soving process and soving accuracy.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - The Algebraical Superposition Technic for Transformation from S Domain to Time Domain
AU  - Benqing Gao
Y1  - 2020/08/17
PY  - 2020
N1  - https://doi.org/10.11648/j.ajmp.20200904.11
DO  - 10.11648/j.ajmp.20200904.11
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 55
EP  - 59
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20200904.11
AB  - An algebraical superposition technic for transformation from frequency domain to time domain is presented. The establishing model process are; From the inverse Laplace transform integral formula, the integral formula can be expressed by the series with k [-K, K] term., based on integral function distribution properties along integral path, the bidirectional series sum on k [-K, K] term series can be expressed by a monomial trigonomial function series sum on k [0, K]. In the paper the solution process and main points are presented. The application examples are shown; the results are supported to the algebraical superposition technic. In using above algebraical superposition technic to analysis airspace dispersive propagation poperties, i.e., to find out its time-domain parameters, the resultant formula contain time-domain factor and frequency-domain factor, that is first time to present in the paper, so it is called ‚’time-frequency union technic‘. In the paper simultaneity solve out wave number and wave impendance for waveguide TE10 mode propagation, and get both time-frequency union values, and show the soving process and soving accuracy.
VL  - 9
IS  - 4
ER  -

Copy | Download