FRI sampling and reconstruction of asymmetric pulses

We consider the problem of modelling asymmetric pulse trains as finite-rate-of-innovation (FRI) signals. In particular, we show that the sum of amplitude-scaled and time-shifted pulses with different asymmetry factors is an FRI signal. Such signals frequently arise in applications such as ultrasound and radio detection and ranging (RADAR) where the received signal has skewed pulses. In this paper, we model the asymmetric component of a pulse using its derivative. A sampling kernel with a sum-of-sincs frequency response is used to measure the samples, and a modified annihilating filter method is applied on the samples to estimate the parameters of the FRI signal. We show accurate reconstruction for signals containing asymmetric Gaussian, Cauchy-Lorentz, and sinc pulses. Analysis of the proposed scheme in the presence of noise shows that the error in the estimated parameters decreases by oversampling the signal.