Dynamic neutron scattering probes unique nanoscale dynamics via measurement of energy exchanged between a sample and the neutrons. The two spectrometers that investigate processes with characteristic times around a nanosecond are backscattering (BS) and neutron spin-echo (NSE). We present a new method for measuring dynamics using an oscillating cosine-like energy-distribution neutron-package at the sample and measure solely the portion scattered into the elastic line. This portion corresponds to elastically scattered neutrons and, in addition, inelastic components that are scattered with a probability directly proportional to the cosine Fourier-coefficients of the exchanged-energy spectrum. The counts at the detector thus correspond to the van Hove intermediate scattering function. We denote this new method as “Fourier transform neutron scattering” (FTNS), it being broadly analogous to IR and Raman spectroscopies. Here, the realization of such a concept is investigated using an oscillating incident beam produced via a precession method and a secondary spectrometer identical to a BS instrument using crystal analyzers. The instrument is denoted “Modulated Intensity with Diffraction Analysis Spectrometer” (MIDAS). However, simpler approaches, e.g., choppers, may also be used for an FTNS instrument. The theory behind MIDAS is presented, supported by numerical calculations and in silico experiments. Finally, we present a Monte Carlo simulation to compare BS and MIDAS spectrometers. This shows that MIDAS has almost 100 times more incident flux than standard BS, but due to the better signal-to-noise ratio of BS, the final information acquisition rate gain of MIDAS is approximately a factor of 2.