Design of optimized radix-2 and radix-4 butterflies from FFT with decimation in time

In the FFT computation, the butterflies play a central role, since they allow calculation of complex terms. In this calculation, involving multiplications of input data with appropriate coefficients, the optimization of the butterfly can contribute for the reduction of power consumption of FFT architectures. In this paper different and dedicated structures for the 16 bit-width radix-2 and radix-4 DIT butterflies are implemented, where the main goal is to minimize the number of arithmetic operators in order to produce power-efficient structures. Firstly, we improve a radix-2 butterfly previously presented in literature, reducing one adder and one subtractor in the structure. After that, part of this optimized radix-2 butterfly is used to reduce the number of real multipliers in the radix-4 butterfly. The main results show that the optimization guarantees reduced power consumption for radix-2 butterfly, when compared with previous works from the literature. Moreover, the use of part of the optimized radix-2 into the radix-4 structure leads to the reduction of power consumption for this structure.