Implementation for two-dimensional FIR filters using the number theoretic transform

This paper presents a new implementation technique for two dimensional(2-D) finite impulse response(FIR) filter of relatively large support region using the number theoretic transform (NTT). This method uses a sectioning procedure and fast computation technique of 2-D digital cyclic convolution(DCC). As the size of 2-D DCC by direct use of the NTT is restricted small, the support region of FIR filter is further restricted. But, in the sectioning procedure, the cyclicity of the 2-D DCC should not always be rectangular. Therefore, we propose a 2-D DCC with skewingly cyclic extension. Using this new 2-D DCC and Agarwal´s 2-D technique of the NTT, we may implement practical 2-D FIR filters with smaller number of computational operations.