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自适应噪声对消在很多领域有着重要应用。为了进行自适应噪声对消，提出了一种新的最速下降算法。该算法主要原理是对多元二次函数进行降维处理，使其变成一元二次函数，再应用抛物线的性质分别循环迭代地求解每一个维度上的极值。在自适应噪声对消应用中，所提算法与传统的自适应算法进行对比，具有收敛速度快，滤波效果好，滤波效果可调节，抗恶劣信噪比以及急剧变化信噪比，不需选择迭代步长，适合计算机和可编程硬件实现等优点。

自适应算法 /  最速下降算法 /  噪声对消 /  最小均方误差 /  自适应滤波器 Abstract:

Adaptive noise cancellation has important applications in many fields. In order to carry out adaptive noise cancellation, a new steepest descent algorithm is proposed. The main principle of the algorithm is to reduce the dimension of multivariate quadratic function to make it become a univariate quadratic function, and then apply the properties of parabola to iteratively solve the extremum of each dimension. Compared with the traditional adaptive algorithm, the new steepest descent algorithm shows the advantages of fast convergence, good filtering effect, adjustable filtering effect, resisting bad SNR and sharp change SNR, no need to choose iteration step, and suitable for computer and programmable hardware implementation.

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