We present an algorithm for the resolution of delayed and overlapping pulses of a common unknown shape from multi- channel measurements. We show that just a few Fourier sam- ples acquired by a Time Encoding Machine (TEM) suffice to solve this challenging problem. This acquisition scheme is desired for ultra-low power applications in wearables, such as EMG skin sensor tattoo. Numerical experiments demonstrate exact recovery of the time delays and Fourier series coeffi- cient of the pulse shape in the noiseless case as predicted by the theory, with acceptable error in the presence of noise.