Abstract: There are two classes of power spectrum estimation methods in alpha stable distribution, that are covariation and covariance spectrum estimation. The methods can not be used in time-frequency analysis for they analyze frequency-domain information by auto-correction or its two order moments and lost signal phase information. A novel power spectrum estimation method of fractional lower-order alpha stable distribution is proposed. Simulations show that the proposed method has excellent performance in estimating fractional lower order power spectrum, can be used further in time-frequency analysis and has more widely application value.

Key words: alpha stable distribution, fractional lower-order, covariation spectrum, covariance spectrum, time-frequency analysis

摘要： 传统的[α]稳定分布噪声下信号功率谱估计方法有两种，分别为共变谱估计与协方差谱估计。这两种谱估计方法都是以自相关这个二阶矩作为频域分析对象，而自相关是个损失了信号中相位的信息，不能用于时频域分析。针对这一问题，提出了一种新的分数低阶功率谱估计方法，计算机仿真结果表明，与现有方法相比，该新方法不仅在进行分数低阶功率谱估计时具有更优良的性能，而且可进一步应用于时频域分析，具有更广泛的应用价值。

关键词: [&alpha, ]稳定分布, 分数低阶, 共变谱, 协方差谱, 时频分析