Abstract: A low cost method of adding time-resolving capability to commercial Fourier-transform spectrometers with a continuously scanning Michelson interferometer. This invention is specifically designed to eliminate noise and artifacts caused by mirror-speed variations in the interferometer. The method exists as two parts: 1) a novel timing scheme for synchronizing the transient events under study with the digitizing by an analog-to-digital converter, and 2) a mathematical algorithm for extracting the spectral information from the recorded data. The novel timing scheme is a modification of the well known interleaved, or stroboscopic, method. It achieves the same timing accuracy, signal-to-noise ratio, and freedom from artifacts as step-scan time-resolving Fourier spectrometers by locking the sampling of the interferogram to a stable time base rather than to the occurrences of the HeNe fringes. The necessary path-length-difference information at which samples are taken is obtained from a record of the mirror speed.