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A class of cascade filters, orthogonal with respect to a new inner product, is presented in this paper. A sequence of generalized Malmquist orthogonal rational functions is used for design of these filters. In addition, by using these functions Müntz polynomials which are orthogonal in respect to a special inner product were derived. Obtained Müntz polynomials are applied in determination of outputs of the proposed filters. Depending on whether the design of the filters is performed in the s-domain or complex z-domain, we can derive a class of analogue or digital filters, respectively. Outputs from these filters are orthogonal with respect to the two different inner products. Both classes of filters are practically realized and their application in modeling of continuous-time and discrete-time dynamical systems is given. Obtained results show that there are great agreements between the outputs of models and real dynamical systems.

A New Class of Cascade Orthogonal Filters based on a Special Inner Product with Application in Modeling of Dynamical Systems