This paper presents a parameterized low power design for the one-dimensional discrete Fourier transform (DFT) of variable lengths. By combining the cyclic convolution formulation, block-based distributed arithmetic, dynamic pipeline technique, and Cooley-Tukey decomposition together, we have developed a parameterized hardware design for the DFT of variable lengths ranging from 256 to 4096 points and with different modes of performance, which facilitates the performance-driven design considerations in terms of power consumption and processing speeds. This feature is beneficial to developing a parameterized DFT intellectual property (IP) core for meeting the system requirements of different silicon-on-a-chip applications as compared with the existing fixed length DFT designs.