压缩感知加dft频谱分析中的高精度频率估计

Matteo Bertocco, G. Frigo, C. Narduzzi
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引用次数: 6

摘要

多重正弦波形的精确测量是一个经典的频谱分析问题。基于离散傅里叶变换(DFT)的算法需要处理频谱泄漏,这对振幅估计精度和频率分辨率都有不利影响。识别参数信号模型的方法可以获得更好的频率分辨率,但代价是更大的复杂性。基于压缩感知(CS)的超分辨率算法代表了一种新的非参数替代方案,尽管仍然无法获得连续值频率估计,但它可以显著增加频率网格的密度。最近提出的一种称为连续基追踪(CBP)的算法通过制定更复杂的约束凸优化问题来实现这一目标。除稀疏性外,还考虑了大型有限字典中元素的线性插值。频率估计的不确定性仅受信噪比(SNR)的限制,但从计算的角度来看,该方法的要求相当高。本文提出了一种两级频率估计方法。第一阶段是基于cs的超分辨率算法,该算法为第二阶段提供初始输入,第二阶段沿着CBP的线进行线性插值。将这两个步骤整合为一个有效的算法需要仔细考虑算法参数,下面将对其进行讨论,并给出仿真分析的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
High-accuracy frequency estimation in compressive sensing-plus-DFT spectral analysis
Accurate measurement of a multisine waveform is a classic spectral analysis problem. Algorithms based on the discrete Fourier transform (DFT) need to deal with spectral leakage, which adversely affects both amplitude estimation accuracy and frequency resolution. Approaches where a parametric signal model is identified can achieve much better frequency resolution, at the price of greater complexity. The class of super-resolution algorithms based on compressive sensing (CS) represents a new non-parametric alternative that allows a significant increase in the density of the frequency grid, although continuous-valued frequency estimates still cannot be obtained. A recently proposed algorithm called continuous basis pursuit (CBP) achieves this goal by formulating a more complex constrained convex optimization problem. In addition to sparsity, linear interpolation of elements from a large finite dictionary is considered among the conditions. Frequency estimation uncertainty is then limited only by signal-to-noise ratio (SNR), but the aproach is rather demanding from the computational viewpoint. In this paper a two-stage frequency estimation approach is presented. The first stage is a CS-based super-resolution algorithm, that provides the initial input to the second stage, where linear interpolation is carried out along the lines of CBP. Integration of the two steps into one effective algorithm requires some careful consideration of algorithm parameters, which is discussed in the following together with results obtained by simulation analysis.
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