 For the 2D case, and assuming that formula_118 is pre-computed, the number of real multiplications needed to compute formula_61 is

formula_120xformula_46xformula_49xformula_123formula_46xformula_49 formula_126 formula_120xformula_46xformula_49; formula_46 and formula_49 are powers of 2

The arithmetic complexity of the DFT implementation of an FIR filter is effectively independent of the order of the filter, while the complexity of a direct convolution implementation is proportional to the filter order.So, the convolution implementation would be more efficient for the lower filter order.As, the filter order increases, the DFT implementation would eventually become more efficient.