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

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

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

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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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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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.
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Author Information
• Beijing Institute of Technology, School of Information Science and Technology, Beijing, China

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