Discrete Hartley Transform (DHT) is an important tool in digital signal processing. In the present paper, the DHT is firstly transformed into the first-order moments-based form, then a new fast algorithm is proposed to calculate the first-order moments without multiplication. Based on the algorithm theory, the corresponding hardware architecture for DHT is proposed, which only contains shift operations and additions with no need for multipliers and large memory. To verify the availability and effectiveness, the proposed design is implemented with hardware description language and synthesized by Synopsys Design Compiler with 0.18-μm SMIC library. A series of experiments have proved that the proposed architecture has better performance in terms of the product of the hardware consumption and computation time.
This paper presents hardware efficient designs for implementing the one-dimensional (1D) discrete Fourier transform (DFT). Once DFT is formulated as the cyclic convolution form, the improved first-order moments-based cyclic convolution structure can be used as the basic computing unit for the DFT computation, which only contains a control module, a barrel shifter and (N-1)/2 accumulation units. After decomposing and reordering the twiddle factors, all that remains to do is shifting the input data sequence and accumulating them under the control of the statistical results on the twiddle factors. The whole calculation process only contains shift operations and additions with no need for multipliers and large memory. Compared with the previous first-order moments-based structure for DFT, the proposed designs have the advantages of less hardware consumption, lower power consumption and the flexibility to achieve better performance in certain cases. A series of experiments have proven the high performance of the proposed designs in terms of the area time product and power consumption. Similar efficient designs can be obtained for other computations, such as DCT/IDCT, DST/IDST, digital filter and correlation by transforming them into the forms of the first-order moments based cyclic convolution.