An improved crest factor minimization algorithm to synthesize multisines with arbitrary spectrum
An improved crest factor minimization algorithm to synthesize multisines with arbitrary spectrum
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DOI：
10.1088/0967-3334/36/5/895
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发表时间：
2015-04
影响因子：
3.2
通讯作者：
Yuxiang Yang;Fu Zhang;Kun Tao;B. Sanchez;He Wen;Zhaosheng Teng
中科院分区：
文献类型：
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作者：
Yuxiang Yang;Fu Zhang;Kun Tao;B. Sanchez;He Wen;Zhaosheng Teng
低波峰因数的多正弦信号具有较高的信噪比，可用于快速频率响应函数估计。具有给定幅度谱的低CF多正弦的合成取决于其余弦分量的初始相位的最佳选择。研究的解一般可分为两个分支：（1）基于直接公式计算的解析方法;（2）基于迭代计算的数值方法。分析方法仅适用于等距和平坦的振幅谱，而数值方法通常可以输出更好的结果，即使对于稀疏或非平坦的谱，但迭代次数可能很大。将Schroeder分析法与货车der Ouderaa（VDO）迭代法相结合，提出了一种改进的CF最小化算法，用于合成多正弦信号。该算法采用Schroder相位作为迭代初始相位，并在VDO迭代过程中采用迭代指数为i的对数裁剪函数。对三种余弦振幅谱进行了多正弦合成的综合实验，与以往的方法相比，所得到的CF在所有情况下都保持最低水平。该算法提供了一种快速有效的解决方案，以合成多正弦与最低的CF为任意用户指定的频谱。
Multisine signal with a low crest factor (CF) can bring a high signal-to-noise ratio for fast frequency response function (FRF) estimation. Synthesis of a low CF multisine with the given amplitude spectrum depends on optimum selection of the initial phases of its cosinusoidal components. The solutions investigated can be generally divided into two branches: (1) the analytical method based on direct formula calculation; and (2) the numerical method based on iterative computations. The analytical method works well only for an equidistant and flat amplitude spectrum, while the numerical method can generally output better results, even for a sparse or non-flat spectrum, but the number of iterations might be huge. This paper presents an improved CF minimization algorithm to synthesize multisine signals based on the combination of the previous Schroeder analytical method and the Van der Ouderaa (VDO) iteration procedure. The improved algorithm adopts the Schroder phases as the iterative initial phases, and employs a logarithmic clip function of the iterative index i in the VDO iteration procedure. Comprehensive experiments of multisine synthesis on three types of cosinusoidal amplitude spectra are performed, and the resulting CFs remain the lowest level in all cases compared with the earlier methods. The proposed algorithm provides a fast and efficient solution to synthesize multisine with the lowest CF for an arbitrary user-prescribed spectrum.