TIME DOMAIN RECURSIVE DIGITAL FILTER MODELING BASED ON RECURRENT NEURAL NETWORK TRAINING
Stela Angelova Stefanova · 2004
In this paper a time domain recursive digital filter model, based on recurrent neural network is proposed. This problem can be considered as a training procedure of two layer recurrent neural network. The proposed neural network training algorithm is based on determination of the sensitivity coefficients of the recurrent system. The dynamic model of two layer recurrent neural network described by system of recurrent equations is considered. Time domain modeling approach has been applied to design the Nyquist recursive digital filter. Digital filter parameters are obtained by optimization procedure when the requirements to the impulse response in time domain are given. Modern devices for digital signal processing in particular digital filters represent dynamical systems described with the difference equations. This fact allows the application of neural networks for defining the design problem in time domain, for modeling and realization of the non-recursive (finite impulse response – FIR), recursive (infinite impulse response – IIR) and adaptive digital filters (DF). One approach for the 1-D FIR digital filter design based on the weighted mean square method and neural network to state the approximation problem is proposed in [1]. Some methods for the non-linear digital filters design using neural networks are considered in [2]. Basic results related to the discrete dynamical systems approximation using neural networks are discussed in [3]. In this paper a 1-D IIR digital filter neural network model is proposed. Training sequences of input excitations and corresponding filter responses are generated for the training procedure of this model with given neural network structure. The digital filter model has been trained in such a way that with given predetermined input signal, the output variable approximates the target function in mean square sense. Time domain modeling approach has been applied to design the Nyquist recursive digital filter. Digital filter parameters are obtained by optimization procedure when the requirements to the impulse response in time domain are given. 1. RECURSIVE DIGITAL FILTER MODELING BASED ON NEURAL NETWORK The neural network structure used for the recursive digital filter modeling is