On the application of the jackknife to the estimation of the parameters of short multisinusoidal signals using the data-matrix formulation

It is demonstrated that the jackknife can be applied to the estimation of the parameters of a single short segment of a noisy, complex multisinusoid signal where the estimation process itself is based on the data-matrix formulation. The parameters of interest are the frequency, amplitude, and initial phase of each sinusoid, and the key role of the jackknife is to provide an estimate of the standard deviation of the estimates of these parameters from the single record available. The jackknife is shown to be especially appropriate where the primary estimator is well-behaved and its performance is broadly optimum where the sub-segment length used in creating the data matrix is about one-half of the record length and improves somewhat as the data length itself increases. This is inferred from a series of simulations involving three different algorithms with one, two, and three complex sinusoids in complex white noise. The application of the jackknife in the presence of phase noise and additive colored noise is also briefly examined. Due to the correlation between the columns of the data matrix, the successful application of the jackknife to this problem cannot be assumed a priori.<
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