谐波过程的高阶广义各态历经性的分析与应用
Analysis and applications of higher-order ergodicity of harmonic process
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摘要: 高阶统计在信号处理的许多领域得到了广泛应用。但在实际应用的许多情况下,由于只能得到观测过程的一个样本,所以只能用样本的时间平均来代替其统计平均。其前提是过程对该统计量具有广义的各态历经性,该文分析了谐波过程高阶统计量的各态历经性,得到了谐波过程满足三阶、四阶矩和累积量广义各态历经的充要条件。然后研究了这些条件在高阶统计量的相位耦合识别、高阶阵列处理方法等问题中的应用,并进行了模拟实验验证。Abstract: The higher-order statistics has found applications in the wide area of signal processing problem. However in some practical applications, only a sample of the objective process can be obtained. Thus the statistical average must be replaced by time average. The precondition to do this is the ergodicity of the processes. The ergodicity of the higher-order statistics of the harmonic processes is analyzed in this paper. Further more, the applications of the ergodicity in the phase coupling recognition and the array processing problems using higher-order statistics are proposed in this paper. Simulation examples verified those results.
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J.M. Mendel, Tutorial on higher-order statistics(spectra) in signal processing and system theory:theoretical results and some applications, Proc. IEEE, 1991, 79(3), 278-305.[2]C.L. Nikias, M. R. Raghuveer, Bispectrum estimation: A digital signal processing framework,Proc. IEEE, 1987, 75(7), 869-891.[3]B. Porat, B. Friedlander, Direction finding algorithms based on high-ordcr statistics, IEEE Trans.on SP, 1991, SP-39(9), 2016-2023.[4]M.C. Dogan, J. M. Mendel, Application of cumulants to array processing Part I: Aperture extension and array calibration, IEEE Trans. on SP, 1995 SP-43(5), 1200-1216. -
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