In reality, the duration of all light sources (oscillators) is finite. So, effectively, light is always pulsed, whether it is of nano second or of giga second durations. This paper develops a conceptually congruent model of propagating the carrier frequency of a generic pulse directly in the time domain through traditional instruments and media. The modeling approach covers all spectrometers like multi-beam Fabry-Perots and gratings, and two-beam Fourier transform spectrometers. The established

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... approach uses a non-causal Fourier integral to generate Fourier decomposed frequencies of the pulse, which exist in all time, and find their steady state delays through instruments and media. This frequency domain approach gives correct results when appropriately used, but encounters contradictions under some situations that are discussed. In contrast, the time-domain analysis, while mathematically less elegant, always makes correct predictions, besides giving us a deeper and better understanding of the physical processes of temporal evolution of the pulse through various instruments.