iMUSIC: A Family of MUSIC-Like Algorithms for Integer Period Estimation
iMUSIC: A Family of MUSIC-Like Algorithms for Integer Period Estimation
复制标题
DOI：
10.1109/tsp.2018.2879039
复制
发表时间：
2019-01-15
影响因子：
5.4
通讯作者：
Vaidyanathan, Palghat P.
中科院分区：
文献类型：
--
作者：
Tenneti, Srikanth Venkata;Vaidyanathan, Palghat P.
MUSIC算法是目前最流行的线谱估计技术之一。如果线路频谱是周期信号的频谱，我们能否调整MUSIC以利用频谱中的附加谐波？在此方向上重要的前期工作包括Harmonic MUSIC算法及其变体。对于离散信号周期为整数（或可以很好地近似为整数）的应用，本文介绍了一种新的更简单的MUSIC替代方法。这个名为iMUSIC的新家族还包括用简单的整数值向量代替复指数来表示信号子空间和计算伪频谱的技术。结果表明，所提出的方法不仅使计算比先前的MUSIC周期自适应方法简单得多，而且对于整数周期的应用具有明显更好的估计精度。这些优点在包括蛋白质和DNA序列重复的例子中得到了证明。iMUSIC算法基于最近提出的Ramanujan子空间和嵌套周期子空间。得到的信号空间基在结构上是非范德蒙德的。因此，古典音乐的许多方面是基于复指数的范德蒙德结构，如保证频率的可识别性（在我们的例子中是周期），在本文中以新的方式解决。
The MUSIC algorithm is one of the most popular techniques today for line spectral estimation. If the line spectrum is that of a periodic signal, can we adapt MUSIC to exploit the additional harmonicity in the spectrum? Important prior work in this direction includes the Harmonic MUSIC algorithm and its variations. For applications where the period of the discrete signal is an integer (or can he well approximated by an integer), this paper introduces a new and simpler class of alternatives to MUSIC. This new family, called iMUSIC, also includes techniques where simple integer valued vectors are used in place of complex exponentials for both representing the signal subspace, and for computing the pseudo-spectrum. It will be shown that the proposed methods not only make the computations much simpler than prior periodicity-adaptations of MUSIC, but also offer significantly better estimation accuracies for applications with integer periods. These advantages are demonstrated on examples that include repeats in protein and DNA sequences. The iMUSIC algorithms are based on the recently proposed Ramanujan subspaces and nested periodic subspaces. The resulting signal space bases are non-Vandermonde in structure. Consequently, many aspects of classical MUSIC that were based on the Vandermonde structure of complex-exponentials, such as guarantees for identifiability of the frequencies (periods in our case), are addressed in new ways in this paper.