A general method of deriving a discrete normalized system of orthogonal functions and its application to adaptive digital filters

Abstract

AbstractThe system of orthogonal functions is very useful in science and engineering, and the theory on the orthogonal function system in the continuous time domain has been established. On the other hand, with the advance in digital signal processing, a need for processing the signal in the discrete time domain is acute. With this background, a general derivation of the orthogonal function system in the discrete time domain is desired. This paper proposes a general method for deriving the orthogonal function system in the discrete time domain from the already established orthogonal function system in the continuous time domain. First, the orthogonal function system in the continuous time domain is presented. Next, by the bilinear information of its transfer function, the system is transferred to the discrete time domain. However, in general, the orthogonality in the discrete time domain is destroyed by the bilinear transformation. It is shown that the orthogonality can be maintained in the discrete time domain and the orthonormal function system can be constructed by an appropriate processing. Further, the digital filter using this orthonormal function system is applied to the adaptive digital filter and the number of adaptive parameters is reduced. Finally, by computer simulation, the effectiveness of the adaptive filter configuration by means of the orthonormal function system is proven.