Neural fuzzy digital filtering: Properties

The paper describes the structure of the neural fuzzy filtering; giving an approach of this kind of filters called NFDF. This filters have an adaptive fuzzy inference mechanism in order to deduce the filter answers to select the best parameter values into the knowledge base (KB), actualizing the filter weights to give a good enough answers in natural linguistic sense; this require that all of the states bound into NFDF error functional, also considering the Nyquist criterion. A conventional filter can't classifies and deduce its responses into levels, the difference with the NFDF is that it characterizes the variables of a reference system and the set of membership functions using levels of response into the KB describing the classification of the filter using its probabilistic properties with respect to the rules set decisions, performing the NFDF. The paper also describes illustratively the neural net architecture into the filter mechanism. The results expressed in formal sense by the definitions related in the papers included into the paper references. Finally, the paper shows schematically the NFDF operation applying the first order ARMA model as reference system using the Matlab copy software.