Multichannel Fourier transform interferometry to measure the spectrum of arbitrarily short pulses and of fast time-varying signals was achieved using a micro/nanomanufactured multimirror array. We describe the performance of a demonstrator FTIR that works in the mid-infrared (MIR) range of 700-1400 cm(-1) and reaches a spectral resolution of 10 cm(-1) taking into account apodization. Spectral measurements down to pulse lengths of 319 µs were carried out using a mechanical camera shutter. Arbitrarily short pulses are expected feasible provided the source can deliver enough photons to overcome the noise equivalent number of photons.