New algorithm for spectral factorization and its practical application

In this report a new algorithm is presented for the spectral factorization of a two-sided symmetric polynomial. The method is based on the discrete Fourier transform theory (DFT) and its relationship to the Z-transform. Involving DFT computational techniques, namely the famous fast Fourier transform routine (FFT), brings high computational efficiency and reliability. The power of the proposed procedure is employed in a particular practical application. Namely the problem of computing an H₂-optimal inverse dynamic filter to an audio equipment is considered as it was proposed by M. Sternad and colleagues in [12] to improve behavior of moderate quality loudspeakers. Involved spectral factorization is resolved by our new method and its performance is compared with existing algorithms.