A new technique for power spectrum estimation using multirate observations
ASID'09 Proceedings of the 3rd international conference on Anti-Counterfeiting, security, and identification in communication
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In this paper, we are interested in estimating the power spectral density of a stationary random signal x(n) when the signal itself is not available but some low-resolution measurements derived from it are observed. We consider a model where x(n) is being measured using a set of linear multirate sensors. Each sensor outputs a measurement signal vi(n) whose sampling rate is only a fraction of the sampling rate assumed for the original signal. Based on this model, we pose the following problem: Given certain autocorrelation coefficients of the observable signals vi(n), estimate the power spectral density of the original signal x(n). It turns out that this problem is ill-posed. We suggest to resolve this issue by using the principle of maximum entropy (ME). We address technical difficulties associated with the ME solution and then devise a practical algorithm for its approximate computation. We demonstrate the viability of this algorithm through simulation examples.