Restoring a δ-pulse train by spectral fitting

The problem of restoring a δ-pulse train h(t ) from its bandpass filtered and noise-corrupted version is considered. A spectral fitting approach is described which fits terms of the form ρ_ke exp(-jωτk) to the estimated spectrum of h(t). This fitting problem can be efficiently solved using the FFT algorithm. The error in the estimated pulse positions is discussed by analyzing the fluctuation of the peak position of the cross correlation function. Computer simulation results are presented which indicate the validity of these calculations and analyses