A real-time algorithm for Time Decoding Machines

Time-encoding is a real-time asynchronous mechanism of mapping the information contained in the amplitude of a bandlimited signal into a time sequence. Time decoding algorithms recover the signal from the time sequence. Under an appropriate Nyquist-type rate condition the signal can be perfectly recovered. The algorithm for perfect recovery calls, however, for the computation of a pseudo-inverse of an infinite dimensional matrix. We present a simple algorithm for local signal recovery and construct a stitching algorithm for real-time signal recovery. We also provide a recursive algorithm for computing the pseudo-inverse of a family of finite-dimensional matrices.