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Smoke and Mirrors: Ultra-Rapid-Scan FT-IR Spectrometry

In principle it, is simple to reconstruct the original laser signal from the undersampled data. This is possible because there are no frequency components, other than noise, present below the Nyquist limit at times when the mirror motion produces an optical velocity above 158 cm/s. If these regions of the data are clipped out and Fourier transformed, the frequency spectrum of the original signal can be reconstructed by a mirroring operation about the original Nyquist limit. The inverse Fourier transform of the original frequency spectrum reproduces the original time domain signal, which can then be spliced back into the time series.

 
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