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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