  We present a harmonic model for the data analysis of an all-sky cosmic
microwave background survey, such as Planck, where the survey is obtained
through ring-scans of the sky. In this model, resampling and pixelisation of
the data are avoided. The spherical transforms of the sky at each frequency, in
total intensity and polarization, as well as the bright-point-source catalogue,
are derived directly from the data reduced onto the rings. Formal errors and
the most significant correlation coefficients for the spherical transforms of
the frequency maps are preserved. A clean and transparent path from the
original samplings in the time domain to the final scientific products is thus
obtained. The data analysis is largely based on Fourier analysis of rings; the
positional stability of the instrument's spin axis during these scans is a
requirement for the data model and is investigated here for the Planck
satellite. Brighter point sources are recognised and extracted as part of the
ring reductions and, on the basis of accumulated data, used to build a
catalogue. The analysis of the rings is performed iteratively, involving a
range of geometric and detector response calibrations. The reconstructed
spherical transforms of the sky form the input to the subsequent analysis
stages. Although the methods in this paper were developed with the data
processing for Planck in mind, many aspects should have wider application, such
as in the construction of real-space pixelised maps. (Abridged)
