Exponential estimation of the unknown frequencies of discrete-time multi-tone sinusoidal signals

While the estimation problem of the unknown frequencies for a continuous-time multi-tone sinusoidal signal was thoroughly solved in the early 2000s, the discrete-time version of this problem was studied only recently via a nonlinear control approach. In this paper, we present a simpler approach to the estimation problem of the unknown frequencies for a discrete-time multi-tone sinusoidal signal. Our approach only involves the design of two linear filters together with a linear adaptation law. As a result, the implementation of our two linear filters is easier than that of nonlinear ones. Moreover, the linear form of our filters lends itself to the establishment of the exponential convergence of the estimated frequencies to their actual values. In addition, we obtain an interesting exponential stability result for a class of discrete-time linear time-varying systems that can be viewed as a discrete-time counterpart of a well-known stability result arising from continuous-time adaptive identification. (C) 2021 Elsevier Ltd. All rights reserved.