In long haul communication environments, speech data transmission is severely affected by echoes. This phenomenon results in high bit errors as well as in degraded and annoying performance. Traditionally these problems, including hybrid and acoustic echoes, have been controlled through the use of echo suppressors. These suppressors were subsequently replaced by line echo cancellers using adaptive Finite Impulse Response filters. Fractional calculus has been applied successfully for fixed filtering with constant coefficients and in discrete time adaptive filtering that adjusts the weights according to the environment. This paper presents the Fractional Least Mean Square (FLMS) and Fractional Normalized LMS (FNLMS) algorithms for application in echo cancellation. Moreover, the performances of the FLMS and FNLMS are compared with those provided by the standard LMS, NLMS and Block Discrete Fourier Transform solutions. The mean square error criterion is used as the performance comparison criterion for two types of voice signals namely real and synthetic. The simulation results show a performance improvement of about 50% over the traditional counterparts.

在长距离通信环境中，语音数据传输会受到回声的严重影响。这种现象会导致较高的误码率，并导致性能下降和令人讨厌。传统上，这些问题，包括混合回声和声学回声，都是通过使用回声抑制器来控制的。随后，使用自适应有限脉冲响应滤波器将这些抑制器替换为线路回声消除器。小数演算已成功应用于具有恒定系数的固定滤波以及可根据环境调整权重的离散时间自适应滤波。本文提出了分数最小均方（FLMS）和分数归一化LMS（FNLMS）算法在回声消除中的应用。此外，将FLMS和FNLMS的性能与标准LMS，NLMS和块离散傅立叶变换解决方案提供的性能进行了比较。均方误差准则用作两种类型的语音信号（即真实和合成）的性能比较准则。仿真结果表明，与传统的同类产品相比，性能提高了约50％。