A stochastic realization algorithm via block LQ decomposition in Hilbert space
A stochastic realization problem of a stationary stochastic process is re-visited, and a new stochastically balanced realization algorithm is derived in a Hilbert space generated by second-order stationary processes. The present algorithm computes a stochastically balanced realization by means of the singular value decomposition of a weighted block Hankel matrix derived by a ''block LQ decomposition''. Extension to a stochastic subspace identification method explains how the proposed abstract algorithm is implemented in system identification.
The generation and behavior of the fractal Koch array factor from a Kaiser window generator is studied. The main advantage of using Kaiser windows is that pattern parameters become much more flexible through altering the Kaiser window. The mainlobe width, current distribution, side-lobe ratio are now adjustable. Different reduced array structures can be obtained by using different threshold levels. Higher threshold values result in a highly reduced number of elements but they may highly distort the pattern and, hence, the multiband behavior. Finally, we study the effect of quantization of the feeding values. Quantization is necessary for implementation and simplification purposes. Several configurations of current distributions with the corresponding patterns are illustrated for different quantization levels. It is shown that moderate quantization keeps the same interesting similarity properties at several bands.