Asymptotic Performance for Delayed Exponential Process

The damped and delayed sinusoidal (DDS) model can be defined as the sum of M sinusoids whose waveforms can be damped and delayed. This model is suitable for compactly modeling short time events. This property is closely related to its ability to reduce the time-support of each sinusoidal component. In this correspondence, we derive exact and approximate asymptotic Crameacuter-Rao bounds (CRBs) for the DDS model. This analysis shows that this model has better, or at least similar, theoretical performance than the well-known exponentially damped sinusoidal (EDS) model. In particular, the performance in the DDS case is significantly improved compared to that of the EDS for closely spaced sinusoids thanks to the nonzero time delays. Consequently, we can exploit the advantageous properties of the DDS model and, in the same time, we can keep high theoretical model parameter estimation accuracy