FFT based algorithm for polynomial plus-minus factorization

In this report a new algorithm is presented for the plus/minus factorization of a scalar discrete-time 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 effectiveness of the proposed algorithm is demonstrated by 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 [16] to improve behavior of moderate quality loudspeakers. Involved spectral factorization can be converted into plus-minus factorization in a special case which in turn is resolved by our new method.