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实离散Fourier变换（RDFT）是1985年Ersoy提出的一种实变换，在许多信号处理应用中其性能优于离散Founier变换（DFT）．本文建立了实数LMS自适应算法与RDFT之间的联系，提出了利用实数LMS自适应滤波器计算RDFT与DFT的一种方法．该算法与Widrow算法不同，把RDFT的实数变换核作为自适应滤波器的输入矢量，用实数LMS自适应算法进行计算．整个过程仅涉及实数运算，所需存贮单元的数目只有Widrow算法的一半．当计算实序列DFT时，实乘次数只有Widrow算法的三分之一，实加次数不到Widrow算法的五分之一；而计算复序列DFT时，实乘次数也只有Widrow算法的三分之二，实加次数还不到Widrow算法的五分之三。此算法更适于并行处理与VLSI实现，它为计算RDFT与DFT提供了一条新的神经网络途径．
Real Discrete Fourier Transform (RDFT) is a real transform proposed by Ersoy in 1985 and its performance is superior to discrete Founier transform (DFT) in many signal processing applications. In this paper, we establish the relationship between real LMS adaptive algorithm and RDFT, and propose a method to calculate RDFT and DFT by using real LMS adaptive filter. The algorithm is different from the Widrow algorithm. The real conversion kernel of RDFT is used as the input vector of the adaptive filter, and is calculated by the real LMS adaptive algorithm. The whole process involves only real number operations, and the number of required memory cells is only half that of the Widrow algorithm. When calculating the real sequence DFT, the real number of multiplications is only one-third of the Widrow algorithm, and the actual addition times are less than one-fifth of the Widrow algorithm. When calculating the complex sequence DFT, the real multiplier is only one-third of the Widrow algorithm Second, the actual number of addition less than three-fifths of the Widrow algorithm. This algorithm is more suitable for parallel processing and VLSI implementation, which provides a new neural network approach for computing RDFT and DFT.