利用实数LMS自适应滤波器计算RDFT与DFT

Computation of the RDFT and DFT through the real LMS adaptive filter

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．

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.