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In many areas of signal, system, and control theory, orthogonal functions play an important role in issues of analysis and design. In this paper, we will expand and generalize the orthogonal functions... as basis functions for dynamical system representations. The orthogonal functions can be considered as generalizations of, for example, the pulse functions, Laguerre functions, and Kautz functions. A least-squares identification method is studied that estimates a finite number of expansion coefficients in the series expansion of a transfer function, where the expansion is in terms of recently introduced generalized orthogonal functions. The analysis is based on the result that the corresponding linear regression normal equations have a block Toeplitz structure. It is shown how we can exploit a block Toeplitz structure to increase the speed of convergence in a series expansion.show more
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