Asymptotic Performance for Delayed Exponential Fitting

The Damped and Delayed Sinusoidal (DDS) model is suitable for modeling compactly short time events (as the audio transient for instance). This property is closely related to its ability to reduce the time-support of each sinusoidal component. In this work, we derive an analytical and numerical conditional CRB for this model. In particular, we show that this model has, in general and at least, similar theoretical performance than the well-known Exponentially Damped Sinusoidal model. Moreover, the performances in the DDS case can be improved, compared to those of the EDS case for closely spaced sinusoids. 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. Key-Words: Sinusoidal model, time-delay, Cramer-Rao Bound