New Algorithm for Real-Valued Fourier Transform

This paper presents a direct algorithm for fast real discrete Fourier transform (RDFT) computing, using the discrete Fourier transform (DFT) conjugate symmetric property to reduce redundancies. In RDFT, all the input and output signals were real, which differed from complex DFT. Therefore, the structure of the proposed algorithm showed only real-data operations. The developed algorithm showed the desired properties, such as in-place computation, regularity, simplicity, and arithmetic operations reduction. The RFFT performance was compared with other related transforms, such as the fast Hartley transform (FHT) for the computation in the radix-2 algorithm. It was found that FHT showed the best performance in terms of arithmetic complexity.