Time Encoding Using the Hyperbolic Secant Kernel

We investigate the problem of reconstructing signals with finite rate of innovation from non-uniform samples obtained using an integrate-and-fire system. We assume that the signal is first filtered using the derivative of a hyperbolic secant as a sampling kernel. Timing information is then obtained using an integrator and a threshold detector. The reconstruction method we propose achieves perfect reconstruction of streams of K Diracs at arbitrary time locations, or equivalently piecewise constant signals with discontinuities at arbitrary time locations, using as few as 3K+1 non-uniform samples.