Atmospheric spectra reconstructed from interferometric measurements are susceptible to scene motion, which can be caused by changing environment or instrument jitter. This leads to a coupling between the time series of the modulated scene radiance and the interferogram collected as a function of time. Spectral artifacts are generated when this occurs and appear as both narrow, isolated spikes in the measurement wavelength band as well as broad, out-of-band features. Here, we derive an analytical relationship that depends on jitter frequency, amplitude and phase, and the scene gradient. The observed radiance is expressed as a spatially weighted mixture of radiance originating from various points within the scene. Spectral artifacts created by relative scene motion are shown to be proportional to the radiometric scene difference within the instrument field of view (FOV) and jitter amplitude, and vary significantly with the jitter frequency. The analytical solution can be useful in various applications, where image instability is expected to have an effect on measurements in question, ranging from spectroscopy of turbine plumes, through airborne measurements of smoke density and chemical composition in natural fire or volcanic events, to atmospheric sounding from space.