The effect of multiplexing in Fourier transform spectroscopy (FTS) (and other coding techniques such as Hadamard transform spectroscopy) on the signal/noise ratio arises from two factors. The first of these is a N½ improvement for a spectrum containing N resolution elements since each individual resolution element is now viewed for an N-fold longer time. The second factor is due to the simultaneous observation of all resolution elements, raising the signal level by a factor N for an uniform spectrum.
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T. Hirschfeld (1976) studied this question.