A Class of Almost Orthogonal Filters

In this paper we define a new class of the almost orthogonal filters. These filters are a generalization of the classical orthogonal filters commonly used in the circuit theory, control system theory, signal processing and process identification. Almost orthogonal filters generate the series of almost orthogonal Legendre functions on the interval (0, ∞). They can be successfully used for the analysis, synthesis and designing of imperfect technical systems. They can also be used for approximation of arbitrary functions on (0, ∞). A new method for obtaining the models of imperfect systems is presented as well. Simulations were performed in order to validate the theoretical results and the comparison of new filters with classical filters is given.