## What is it about?

The adaptive Fourier decomposition (AFD) method is an approximation technique of generalized Fourier series, it leads to fast approximations by selecting basis functions in a maximal selection criterion. In recent researches, it has been efficiently applied in identification of linear time-invariant (LTI) systems and new algorithm is named two-step (T-S) algorithm.

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## Why is it important?

In this work, some further modification is made for the T-S algorithm. The improvement is made at the first step, where polynomials are used instead of Cauchy integral formula. By doing this, the algorithm becomes simpler and easier to realize. The approximation errors are analyzed. Due to the analyzed results, this new T-S algorithm is only to get poles for the finite rational orthogonal basis functions but not the approximation to the systems, the coefficients are estimated by using least-squares methods. The effectiveness is examined through numerical examples, that show it takes much less running times and can get comparable approximating results. Besides, the case that errors are included in the frequencies is also studied in this paper, the obtained results imply that minor errors in the frequencies would not affect the estimation.

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## Read the Original

This page is a summary of: On frequency domain identification using adaptive Fourier decomposition method with polynomials, IET Control Theory and Applications, January 2020, the Institution of Engineering and Technology (the IET), DOI: 10.1049/iet-cta.2019.0080.

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