This paper presents a method to analyze and minimize output errors of 2-D non-separable FIR filters with finite wordlength. Finiteness in the wordlength causes output errors, which can be analyzed in the frequency domain when the statistics of input signals are known. The output errors can be minimized by optimizing responses corresponding to all levels of input impulses. A new ROM-based filter structure is proposed in which the optimized impulse responses are stored in the ROM. The output signals are generated by superposing the impulse responses corresponding to the input levels. Many simulation results confirm that the output signals of the proposed filters have far less errors compared to conventional filters. The hardware size of the ROM-based filters is estimated and compared with that of conventional structures. The proposed structures are more effective than the conventional ones especially when the signal wordlength is short.