Alternative methods in spectral factorization. A modeling and design tool. (Q2714919)

Let \(H\) be the transfer function of a linear, causal, stable, minimum-phase single-input single-output system, and let \(A\) be defined by NEWLINE\[NEWLINE A(\omega):= | H(i\omega)| ^2,\qquad \omega \in\mathbb R.NEWLINE\]NEWLINE It is shown that the transfer function \(H\) is uniquely determined by the value \(\arg (H(0))\) and the function \(A\) if \(A\) satisfies the condition NEWLINE\[NEWLINE \int_{-\infty}^{\infty} \frac{| \ln A(\omega)| }{1+\omega^2}\,d\omega\not=\infty.NEWLINE\]NEWLINE In order to show this the authors discuss two alternative contructions of \(H\). One is based on Fourier analysis whereas the second one is based on two-dimensional potential theory. Some applications are given as well.