基于全相位滤波的互素谱分析的高效设计

Efficient design of co-prime spectral analysis based on all-phase filtering

互素谱分析是辨别稀疏样本谱成份的有效途径,然而当前的互素谱分析设计方法存在容易导致频谱泄漏和效率低的缺陷。本文提出基于全相位滤波的高效设计法,首先,分析指出抑制互素谱泄漏的关键在于拓宽原型滤波器的高阻带衰减的频带范围和提升边界频率控制的精度;其次,将基于两种对称频率采样的全相位滤波理论引入到原型滤波器设计中,并推导出滤波器系数解析表达式和与边界频率有关的参数配置公式;最后,将边界频率参数代入到解析表达式中即可实现高性能互素谱分析的高效设计。仿真实验表明,相比于现有的基于等波纹最佳逼近的互素谱设计方法,本文提出的基于全相位滤波的互素谱设计法可更彻底地抑制频谱泄漏,从而提高稀疏样本谱成分的识别准确性。

Co-prime spectral analysis aims to distinguish components in sparse samples. However, the ex- isting co-prime spectra is likely to suffer from spectral leakage and low efficiency. An efficient design based on all-phase filtering is proposed. Firstly, two approaches of suppressing spectral leakage are discovered： broade- ning prototype filters~ stop-band attenuation bandwidths, and improving the precision of the controllable critical frequency. Secondly, all-phase filtering based on two kinds of symmetric frequency sampling is introduced into co-prime spectral analysis, and two analytical formulas of tap coefficients and the critical frequency＇s configura- tion parameters are also derived. Finally, substituting the critical frequency parameters into the chosen formula efficiently completes the final design. Simulation results show that, the proposed method outperforms the equal- ripple filtering based co-prime spectral design in suppressing spectral leakage, thereby enhancing the accuracy of discriminating sparse samples.