Recently, there has been a growing interest within the research community to improve energy efficiency. In this paper, we revisit the classic Fast Fourier Transform (FFT) for energy efficient designs on FPGAs. Parameterized FFT architecture is proposed to identify design trade-offs in achieving energy efficiency. We first perform design space exploration by varying the algorithm mapping parameters, such as the degree of vertical and horizontal parallelism, that characterize the decomposition based FFT algorithms. After empirical selection on the values of algorithm mapping parameters, an energy-performance-area trade-off design for energy efficiency is identified by varying the architecture parameters, including the type of memory elements, the type of interconnection network and the number of pipeline stages. The tradeoffs between energy, area, and time are analyzed using two performance metrics: the Energy×Area×Time (EAT) composite metric and the energy efficiency (defined as the number of operations per Joule). From the experimental results, a design space is generated to demonstrate the effect of these parameters on the various performance metrics. For N -point FFT (16 ≤ N ≤ 1024), our designs achieve up to 28% and 38% improvement in the energy efficiency and EAT, respectively, compared with a state-of-the-art design.