利用递归公式从非均匀采样数据中恢复正弦信号
Retrieving sinusoids from nonuniformly sampled data using recursive formulation
摘要：
一个启发式的程序的基础上，新的递归制定的正弦曲线（RFS）和回归预测最小二乘（LS），使均匀和非均匀采样的1-D信号分解成一个稀疏的正弦曲线（SSS）。通过Levenberg-Marquardt（LM）优化近似最优正弦信号的RFS参数，结合用于估计嵌入噪声中的正弦信号数量的共同标准，找到了最优SSS。该过程估计SSS的基数和参数。所提出的算法能够识别的RFS参数的正弦曲线从一个数据序列只包含一小部分的周期。在极端情况下，当正弦曲线的频率接近零时，该算法能够检测数据中的线性趋势。此外，不规则的采样模式使算法能够正确地重建欠采样的正弦曲线。获得模型的简约性打开了在机器学习和需要分析和1-d信号的简单表示的专家和智能系统中使用所提出的方法的可能性。所提出的算法的属性进行评估的例子不规则采样的人工信号噪声和高精度频率估计算法的基础上线性预测（LP）的方法，特别是相对于克拉美-罗界（CRB）进行比较。
英文摘要：
A heuristic procedure based on novel recursive formulation of sinusoid (RFS) and on regression with predictive least-squares (LS) enables to decompose both uniformly and nonuniformly sampled 1-d signals into a sparse set of sinusoids (SSS). An optimal SSS is found by Levenberg-Marquardt (LM) optimization of RFS parameters of near-optimal sinusoids combined with common criteria for the estimation of the number of sinusoids embedded in noise. The procedure estimates both the cardinality and the parameters of SSS. The proposed algorithm enables to identify the RFS parameters of a sinusoid from a data sequence containing only a fraction of its cycle. In extreme cases when the frequency of a sinusoid approaches zero the algorithm is able to detect a linear trend in data. Also, an irregular sampling pattern enables the algorithm to correctly reconstruct the under-sampled sinusoid. Parsimonious nature of the obtaining models opens the possibilities of using the proposed method in machine learning and in expert and intelligent systems needing analysis and simple representation of 1-d signals. The properties of the proposed algorithm are evaluated on examples of irregularly sampled artificial signals in noise and are compared with high accuracy frequency estimation algorithms based on linear prediction (LP) approach, particularly with respect to Cramer-Rao Bound (CRB).
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