中文摘要：

本文提出了一种基于分形理论的音频频带盲扩展方法。首先，借助重标极差分析法估计频谱细节序列的Hurst指数，对不同音频信号谱细节序列的Hurst指数进行统计分析，验证了音频信号频域序列具有长相关特性。然后，运用坐标延迟法对谱细节序列进行相空间重构，基于夹角余弦选取预测中心相点的近邻点，根据预测中心相点和近邻相点的相关性，求取一个吸引子与预测中心相点相近的迭代函数系统，实现对高频谱细节的分形预测。最后，结合高斯混合模型的高频能量估计算法，实现宽带向超宽带的扩展算法。主、客观质量评测均表明本文算法优于传统的频带盲扩展方法。

英文摘要：

In this paper a new bandwidth extension method of audio signal based on fractal theory was proposed. Firstly, Hurst exponent of the fine spectrum was estimated by means of rescaled range analysis, and the long-range dependence of the fine spectrum was statistically verified based on Hurst exponent of the fine spectrum from different audio signals. Then, the phase space of the fine spectrum of audio signal was reconstructed by delay-coordinate method, and the neighbor phase points were selected with angle cosine. The iteration function system whose attractor was similar with the center phase point was calculated by the neighbor phase points, according to the dependency between the center phase point and the neighbor phase points. A fractal prediction model was established to recover the fine spectrum of high-frequency components of audio signals further. Finally, by combining with the high frequency energy estimation of Gaussian mixture model, the bandwidth of audio signals was extended to super-wideband from wideband. Both the objective and subjective test results demonstrate that the proposed algorithm outperforms the conventional blind bandwidth extension algorithms.