Strong consistency and asymptotic normality are derived for the maximum-likelihood estimates (MLEs) of the unknown parameters ( omega /sub 1/,. . ., omega /sub p/), ( alpha /sub 1/,. . ., alpha /sub p/), and sigma /sup 2/ in the superimposed exponential model for signals, Y/sub t/= Sigma alpha exp (it omega /sub k/)+e/sub t/, where the summation is from k=1 to p, t=0, 1, . . ., n-1, and sigma /sup 2/ is the variance of the complex normal distribution of e/sub t/. As a by-product, it is found that the MLEs of the parameters attain the Cramer-Rao lower bound for the asymptotic covariance matrix.
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机译：对于未知参数（omega / sub 1 /，..，omega / sub p /），（alpha / sub 1 /，..，alpha）的最大似然估计（MLE）得出强一致性和渐近正态性/ sub p /）和信号的叠加指数模型中的sigma / sup 2 /，Y / sub t / = Sigma alpha exp（欧米茄/ sub k /）+ e / sub t /，其中求和来自k = 1至p，t = 0，1，，。 。 ，n-1和sigma / sup 2 /是e / sub t /的复正态分布的方差。作为副产品，发现参数的MLE达到渐近协方差矩阵的Cramer-Rao下界。
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