Keywords: class-spectral-axis-v12

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## Periodic shift and dilatation of the rest frequency axis

For a Earth-based observatory, the observed velocity of the source changes with time due to the rotation of the Earth around its axis and around the sun. This implies that the change from the observatory to the rest frame varies with time. The frequency scale in the observatory frame is fixed by the hardware. The frequency scale in the rest frame thus changes with time in two different ways, a shift and a dilatation. The tuned rest frequency is shifted, while the frequency resolution dilates the frequency axis around the tuned frequency.

If nothing is done, averaging spectra to increase the signal-to-noise ratio would imply first a resampling to align the observed frequency scales. It is desirable to avoid this because resampling has many unwanted side-effects, as round-off errors or introduced correlations of the noise levels between channels (see IRAM Memo 2009-4). We present here hardware solutions to this problem.

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