Algorithms and pipeline architectures for 2-D FFT and FFT-like transforms

In this paper, efficient pipeline architectures that implement the 2-D FFT are presented. Based on the Vector Radix approach, the new structures alleviate the use of memory banks and the transposition of data of the row–column technique. Architectures for Vector Radix 2×2 algorithm and for a modified Vector Radix 4×4, called Vector Radix 22×22 algorithm, which has been devised and constructed from Vector Radix 2×2, are presented. These architectures can also be built from their 1-D counterparts. Thus, generic and parameterised architectures can be described using a hardware description language to implement both 1-D and 2-D FFTs. A comparison with row–column FFT architectures has shown that the proposed architectures can achieve a 50% reduction in complex multipliers usage. Furthermore, the suggested architectures are suitable to implement FFT-like transforms if the right type of arithmetic components is selected. In particular, they can be modified in order to implement Number Theoretic Transforms. In this case, a saving of up to 66% of registers and 50% of adders requirements of similar work in the literature can be achieved.