This paper presents a hardware-efficient design for the one-dimensional (1-D) discrete Fourier transform (DFT). Once
the 1-D DFT is formulated as the cyclic convolution form, the first-order moments-based structure can be used as the
basic computing unit for the DFT computation, which only contains a control module, a statistical module and an
accumulation module. The whole calculation process only contains shift operations and additions, with no need for
multipliers and large memory. Compared with the traditional DA-based structure for DFT, the proposed design has better
performance in terms of the area-throughput ratio and the power consumption, especially when the length of DFT is
slightly longer. Similar efficient designs can be obtained for other computations, such as the DCT/IDCT, DST/IDST,
digital filter and correlation, by transforming them into the forms of the first-order moments-based cyclic convolution.