Asymptotic Performance for Delayed Exponential Process

Remy Boyer (1) , Karim Abed-Meraim (2)

1 L2S - Laboratoire des signaux et systèmes
2 TSI - Département Traitement du Signal et des Images

The damped and delayed sinusoidal (DDS) model can be defined as the sum of 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 Cramér–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.

Domaines: Traitement du signal et de l'image [eess.SP]; Traitement du signal et de l'image [eess.SP]

Remy Boyer, Karim Abed-Meraim. Asymptotic Performance for Delayed Exponential Process. IEEE Transactions on Signal Processing, 2007, 55 (6). ⟨hal-00575668⟩