Spectrum estimation using multirate observations

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 v_i(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 v_i(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.