Thomson's multitaper method estimates the power spectrum of a signal from $N$ equally spaced samples by averaging $K$ tapered periodograms. Discrete prolate spheroidal sequences (DPSS) are used as tapers since they provide excellent protection against spectral leakage. Thomson's multitaper method is widely used in applications, but most of the existing theory is qualitative or asymptotic. Furthermore, many practitioners use a DPSS bandwidth $W$ and number of tapers that are smaller than what the theory suggests is optimal because the computational requirements increase with the number of tapers. We revisit Thomson's multitaper method from a linear algebra perspective involving subspace projections. This provides additional insight and helps us establish nonasymptotic bounds on some statistical properties of the multitaper spectral estimate, which are similar to existing asymptotic results. We show using $K=2NW-O(\log(NW))$ tapers instead of the traditional $2NW-O(1)$ tapers better protects against spectral leakage, especially when the power spectrum has a high dynamic range. Our perspective also allows us to derive an $\epsilon$-approximation to the multitaper spectral estimate which can be evaluated on a grid of frequencies using $O(\log(NW)\log\tfrac{1}{\epsilon})$ FFTs instead of $K=O(NW)$ FFTs. This is useful in problems where many samples are taken, and thus, using many tapers is desirable.

翻译：Thomson的多元图谱方法通过平均摄取量来估计一个信号的电源频谱,这个信号来自$N美元,同样是空间的样本,平均为$K美元。我们用Discrete prolate prolate sperates 序列(DPSS)作为计算器,因为它们提供了极好的保护,防止光谱泄漏。Thomson的多元图谱方法在应用中广泛使用,但大部分现有的理论是定性或无线的。此外,许多实践者使用一个DPSS带宽值$W美元和磁带数比理论所显示的要小得多,因为计算要求随着磁带数的增加而增加。我们从包含子空间预测的线性平方位仪角度重新审视Thomson的多图谱方法(DPSS)。这提供了额外的洞察度方法帮助我们在多波谱光谱估计的某些统计属性上建立非隐含性的界限,这与现有的系统测量结果相似。我们用的是$K=2NF-O(\)美元(NW)美元(NW)的多基),而不是传统的2NW-O(NF),因为计算器可以更好地保护光谱渗漏值,特别是当电谱能谱中我们能够进行一个高的光谱的光谱角度。