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 samples 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 coefficient of the pulse shape in the noiseless case as predicted by the theory, with acceptable error in the presence of noise.