The data are therefore read in the sensor system of coordinates and the outer loop includes, as an initial task, a rotation of these data in an Earth-fixed system using the current values of the quaternions.
Here X is a complex constant which accounts for impedance mismatches in the SMA panel mount connectors and (e^{i phi}) is a rotation of the data relative to the measurement plane [49, 50].
The data for females are rotated slightly with respect to those of males: in most parts of the spectrum, the rotation of the female data is clockwise with respect to the male data – this rotation is implicit in the data and is not the result of an analytic manipulation.
Finally a new algorithm, Principal Phase Correction (PPC) based on principal component analysis, is proposed for phase rotation of CPMG quadrature data, an important prerequisite to optimal SLICING analysis.
Principal Components Analysis is a rotation of the original data in order to orientate the first new axis in the direction of the maximum explained variance.
In the 1970's, the Harrison and Rossmann groups developed 'post-refinement' methods (Rossmann et al., 1979; Winkler et al., 1979), in which the parameters that determine the location and volume of the Bragg peaks are 'post'-refined against a reference set of fully recorded reflections following initial indexing and integration of rotation data.
Through the incorporation of rotation, data can be clustered more appropriately than by standard elliptical basis functions.
These structures, with the exception of 1, were elucidated by comparison of the H and C NMR spectral data and the specific optical rotation of each product with literature data (Tables S1 to S3).
In the present study, we focus on the analysis of the rotation data, with the combination of the translational data recorded in co-location with the rotation sensors.
