Definition of the output spectrum
Keywords: class-average

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Definition of the output spectrum

Let's denote and two spectra that one wants to add, and the output sum. With the `ACCUMULATE` command, and are precisely the corresponding buffers exposed to the user in CLASS. With the `AVERAGE` command, is the average spectrum returned by the loop, and the spectrum in index, with its weight array correctly set. We also call (resp. ) the resolution of (resp. ). This resolution is either in ``number of channels''3, frequency, or velocity per channel depending on the alignment mode (`SET ALIGN CHANNEL|FREQUENCY|VELOCITY` resp.).

From these, the output resolution is taken as the highest of the two (absolute) resolutions in input:

| (1)

This ensures that we never oversample a spectrum which has a low resolution.

The range of abscissa in output spectrum depends on the combination mode:

- `COMPOSITE` mode:

  |  |  | (2)
  |  |  | (3)

- `INTERSECT` mode:

  |  |  | (4)
  |  |  | (5)

Given the output resolution and range, the number of channels can be deduced:

| (6)

where the 1.5 value adds 1 or 2 extra-channels to avoid the erosion of the spectra at the boundaries.

For the oncoming call of the addition routine, we also define the abscissa at the channel used as reference:

| (7)

being the abscissa value of the first channel of the output spectrum. Again, unit is either in ``channels'', velocity or frequency depending on the `SET ALIGN` mode.

This definition of the output spectrum is done only once with the `ACCUMULATE` command. On the other hand with the `AVERAGE` command, the above parameters are revised (if required) each time a new spectrum of the index is added. For example, the output range and number of channels may enlarge (`SET ALIGN * COMPOSITE`) or reduce (`SET ALIGN * INTERSECT`). Also, the resolution is progressively reduced to the coarsest of all the resolutions in the index (eq. ).

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