Multirate Spectral Estimation

Omid S. Jahromi, Bru e A. Fran is, Raymond H. Kwong Systems Control Group, Department of Ele tri al and Computer Engineering, University of Toronto Toronto, ON, M5S 3G4 Canada fomidj, fran is, kwongg ontrol.toronto.edu ABSTRACT This arti le introdu es a mathemati al theory for estimating the power spe tral density (PSD) of a random signal based on low-sampling-rate measurements. We formulate the problem using a mathemati al model where an observer sees a dis rete-time WSS random signal x(n) through a bank of measurement devi es or sensors. Ea h sensor outputs a measurement signal vi(n) whose sampling rate is only a fra tion of the sampling rate assumed for the original non-observable signal. Knowing statisti s of vi(n) is not, in general, suÆient to spe ify the PSD of x(n) uniquely. Therefore, the problem of multirate spe tral estimation is mathemati ally ill-posed. We show that it is possible to onvert the multirate spe tral estimation problem into a mathemati ally well-posed one using the Maximum Entropy prin iple. Moreover, we obtain a losed-form expression for the PSD estimate that results from applying this prin iple and show that it is unique.