Abstract
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.
Highlights
In the fields of electronics, dynamics, controls and other fields of science and technology, the acquirement of system parametersis very important
Realizing the Laplace Transform (LT) between a time domain and frequency domain function by integral form definition is only possible for a one-one regular function pair which often appears in the table of LT function.[1,2,3,4,9]
In order to solve the above difficulties, this paper presents a simple method
Summary
In the fields of electronics, dynamics, controls and other fields of science and technology, the acquirement of system parametersis very important. It is obvious that only a few frequency domain functions mentioned above can obtain their time domain solution by the presented method. In order to solve the above difficulties, this paper presents a simple method. It is not derived from the integral of LT, but by directly processing the object formula in frequency domain to make it transformed into time domain. Take inverse LT on both sides of a frequency domain transcendental equation to obtain a time domain transcendental equation on pending time domain parameter. Re-convolution technic is introduced in the Appendices A–C of the paper, property of time domain sequence obtained is analyzed, and the main points and notices for using re-convolution data are described. The paper uses abbreviations as follows: FD (frequency domain), TD (time domain), LT (Laplace transform), ILT (inverse Laplace transform), RFE (rational fraction expression), IRFE (irrational fraction expression), FDTE (frequency domain transcendental equation), TDTE (time domain transcendental equation), FDS (frequency domain solution), TDS (time domain solution)
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