Positions interpolation

For each spectrum, the Class Data Format expects the following positions:

• lambda offset from reference (usually source) position,
• beta offset,
• azimuth,
• elevation

All these elements are available in the Antenna Slow table, at a typical sampling rate of 1 Hz. Since the spectra dumps can be produced at different time sampling (no assumption is made on the rate or its variations), each spectrum positions are interpolated from the Antenna table thanks to their respective Modified Julian Day values:

$$f = \frac{mjd_S - mjd_A(j)}{mjd_A(j+1) - mjd_A(j)}$$ (5)

where $mjd_S$ is the spectrum MJD value, and $mjd_A(j)$ is the MJD value of the $j^{th}$ trace in the Antenna Slow table. $j$ is computed thanks to a dichotomic search in the table such as:

$$mjd_A(j) \le mjd_S < mjd_A(j+1)$$ (6)

$f$ being the interpolation fraction between the $j^{th}$ and $j+1^{th}$ trace, the positions are interpolated by:

$$l_S = l_A(j) + f \times (l_A(j+1)-l_A(j))$$ (7)

where $l_S$ and $l_A$ are the spectrum and antenna lambda offsets respectively. Same formula applies for the beta, azimuth, and elevation values.

If $mjd_S$ is found beyond the Antenna Slow table limits, the boundary values are applied without extrapolation. However, this is not expected to happen since such spectra should be rejected since they are out of the on-track range.