System Identification With Sparse Coprime Sensing

Abstract

Given a continuous time LTI system with impulse response h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> (t), it is shown that the uniformly spaced samples h <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> (nT) can be identified for any chosen spacing T by using an impulse train input with an arbitrarily small rate 1/NT and sampling the system output with an arbitrarily small rate 1/MT , provided M and N are coprime. This idea, referred to here as the sparse coprime sensing method for system identification, is closely related to well known results in multirate signal processing. It is shown that the problem can be related to the identification of a decimation filter from input-output measurements. It is also shown that the problem is equivalent to the identification of a discrete time N × M LTI system from a knowledge of the full rate input and output vector sequences.