A new principle technic for the transformation from frequency domain to time domain

• Main Author: Ben-Qing Gao
• Format: Article
• Language: English
• Published: AIP Publishing LLC 2017-03-01
• Series: AIP Advances
• Online Access: http://dx.doi.org/10.1063/1.4979327

A principle technic for the transformation from frequency domain to time domain is presented. Firstly, a special type of frequency domain transcendental equation is obtained for an expected frequency domain parameter which is a rational or irrational fraction expression. Secondly, the inverse Laplace transformation is performed. When the two time-domain factors corresponding to the two frequency domain factors at two sides of frequency domain transcendental equation are known quantities, a time domain transcendental equation is reached. At last, the expected time domain parameter corresponding to the expected frequency domain parameter can be solved by the inverse convolution process. Proceeding from rational or irrational fraction expression, all solving process is provided. In the meantime, the property of time domain sequence is analyzed and the strategy for choosing the parameter values is described. Numerical examples are presented to verify the proposed theory and technic. Except for rational or irrational fraction expressions, examples of complex relative permittivity of water and plasma are used as verification method. The principle method proposed in the paper can easily solve problems which are difficult to be solved by Laplace transformation.