| As one of the important branches in the field of signal processing, adaptive filtering theory has been developed and combined with practical application for years. The least mean square (LMS) algorithm based on steepest descent method is widely applied in a lot of fields owing to its simple process and good realizability. However, people also find the obvious weakness, that is the slow convergence rate and the incompatibility problem between stability and convergence rate cause by fixed step sizeμ. In order to overcome the contradiction, new methods are sought, changing into frequency domain to reduce the correlation or using variable step size.Transform domain LMS algorithm can achieve the goal of improving the convergence rate by decorrelating the input signal through a kind of orthogonal transformation to reduce the eigenvalue distribution of the autocorrelation matrix. The best orthogonal transformation is Karhunen-Loeve transformation (KLT), but its transform matrix is overly dependent on the input signal, and can’t be operated in real-time. Discrete cosine transform (DCT) is an approximation of KLT, and has fast algorithm, it is often used in transform domain adaptive filter, especially in the field of speech denoising and image processing. DCT is introduced to LMS algorithm in this paper, the analysis and experiment results show that, its good decorrelation ability improves the convergence rate of the algorithm effectively.At last, a transform domain LMS algorithm based on DCT and a improved variable step-size LMS algorithm based on Sigmoid function are combined to get a new variable step-size LMS algorithm based on DCT, then applied in adaptive noise cancellation system to denoise the voice signal. The results show that, the new algorithm combines the merits of the two, it improves the performance of the classical LMS algorithm comprehensively, with a fast convergence rate, a small steady state misadjustment and a strong anti-noise ability. |
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