A neural networks approach (NNA) was presented to design two-dimensional (2-D) linear-phase finite-impulse response (FIR) digital filters with quadran-tally symmetric magnitude response. To illustrate the feasibility of the NNA, a back-propagation neural-networks (BPNN) model was chosen and the stability of the BPNN was proved. The solution is presented as a parallel algorithm to approximate the desired magnitude response specification. Thus, the method avoids matrix inversion, and makes a fast calculation of the filter's coefficients possible. The implementation of the approach was described together with some design guidelines, and optimal design examples were also given to demonstrate the effectiveness of the proposed approach.
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