Frequency domain identification using adaptive Fourier decomposition method with polynomials

The adaptive Fourier decomposition method is an approximation technique of generalised Fourier series, it leads to fast approximations by selecting basis functions in a maximal selection criterion. In recent research studies, it has been efficiently applied in the identification of linear time-invariant systems and a new algorithm is named two-step (T-S) algorithm. 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 realise. The approximation errors are analysed. Owing to the analysed 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, the obtained results imply that minor errors in the frequencies would not affect the estimation.