在有色高斯噪声中离散时间检测和估计的性能分析
THE PERFORMANCE ANALYSIS OF DISCRETE-TIME DETECTION AND ESTIMATION IN COLOUR GAUSSIAN NOISE
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摘要: 本文研究了在确定的观察时间内,在有色高斯噪声中离散时间检测和估计的性能与样本数之间的关系。指出相邻样本之间相关系数在0.10.2范围内,广义信噪比就能相当接近极限值S2(T)。在讨论二阶相关噪声时指出,由二阶微分方程描写的高斯过程的样本序列一般不是AR(2)模型,但是当样本间隔△0时,却可用AR(2)模型近似描写序列,因此求极限信噪比时,可以较简便地采用AR(2)模型。最后指出最大似然估计与似然比检验之间和两者的性能测度之间的联系。
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Abstract: The relation between the sample number and the performances of signal detection and paramater estimation in correlative Gaussian noise in fixed time T is investigated. It is pointed out that when the autocorrelation coefficient between the neighbour samples in the range of 0.1-0.2, the general SNR S2[T(XL)] will approach to the limit of SNR S2(T). It is also pointed out that the sample sequences of the solution of a second order differential equation generally is not an AR(2) model. But when the sample interval △0, the sample sequences can be described by AR(2). Therefore, S2(T) can be easily calculated. Finally, the relation between likelihood ratio detection and the maximum likelihood estimation is discussed. -
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