The fast Slepian transform
The fast Slepian transform
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DOI：
10.1016/j.acha.2017.07.005
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发表时间：
2016-11
影响因子：
2.5
通讯作者：
Santhosh Karnik;Zhihui Zhu;M. Wakin;J. Romberg;M. Davenport
中科院分区：
文献类型：
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作者：
Santhosh Karnik;Zhihui Zhu;M. Wakin;J. Romberg;M. Davenport
离散长椭球序列（DPSS）提供了一个有效的表示离散信号，是完美的时间限制和近带限。由于投影到DPSS基（也称为Slepian基）上的计算复杂度很高，这种表示往往被忽略，而倾向于快速傅立叶变换（FFT）。我们表明，存在快速的结构计算近似投影到领先的Slepian基础元素。所得到的算法的复杂性是可比的FFT，并顺利地规模所需的近似的质量增加。在限制算法复杂性的过程中，我们还建立了离散时频局部化算子特征值分布的新的非渐近结果。然后，我们演示了这些算法如何使我们能够有效地计算在信号处理中出现的某些最小二乘问题的解决方案。我们还提供了模拟比较这些快速，近似Slepian方法精确Slepian方法以及传统的基于FFT的方法。
The discrete prolate spheroidal sequences (DPSS's) provide an efficient representation for discrete signals that are perfectly timelimited and nearly bandlimited. Due to the high computational complexity of projecting onto the DPSS basis – also known as theSlepian basis– this representation is often overlooked in favor of the fast Fourier transform (FFT). We show that there exist fast constructions for computing approximate projections onto the leading Slepian basis elements. The complexity of the resulting algorithms is comparable to the FFT, and scales favorably as the quality of the desired approximation is increased. In the process of bounding the complexity of these algorithms, we also establish new nonasymptotic results on the eigenvalue distribution of discrete time–frequency localization operators. We then demonstrate how these algorithms allow us to efficiently compute the solution to certain least-squares problems that arise in signal processing. We also provide simulations comparing these fast, approximate Slepian methods to exact Slepian methods as well as the traditional FFT based methods.