Abstract: The real discrete Fourier transform (RDFT) is a real transform introduced by Ersoy in 1985.The RDFT has been found superior to the discrete Fourier transform (DFT) in signal processing applications.A relation between the real LMS adaptive algorithm and the RDFT is established.A new algorithm is proposed to compute the RDFT and DFT via the real LMS adaptive filter.Instead of Widrow's approach,the real transform kernel of the RDFT serves as the input vector of the real LMS adaptive filter.All the operations involved are real.As compared with Widrow's algorithm,the proposed algorithm reduces the storage by a factor of 2.For the real-value DFT,it requires one-third as many real multiplications and slightly less than onesfifth as many additions.For the complex DFT,it requires two-third as many multiplications and less than three-fifth as many additions.The proposed algorithm is applicable to purallel processing and to VLSI implementation.It provides a neural net approach to the RDFT and DFT.