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Two-dimensional digital filters are one of the most fundamental and most important processing techniques in digital vision and image processing and other 2-D digital signal processing fields. This paper studies the relations between the amplitude performances of the 2-D FIR filters and the compound-cosine-based neural network in details. A compound-cosine-based neural network for the design of 2-D filters is proposed. It conquers the main disadvantages of the conventional methods. The convergence theorem, which ensures this neural network convergent, is presented, and the theorem is proved in this paper. The simulation attains near ideal filter characteristics.