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In this paper, we give a new extended and unifying system identification technique for a class of systems that include all main signal models that arise in the Harmonic Decomposition Problem. This technique unifies and extends the previously developed system identification techniques which are improvements on the PISARENKO (MUSIC, dually) Harmonic Decomposition as they arise in arrays of sensors. This technique can be utilized to determine the dominant modes of vibrations of flexible structures as well. An anology is established between arrays of sensors for target signal returns and those that can be used for vibrations in flexible structures.