non_orth.m
Non-orthogonal channel distortion model. Treats odd rows of multi-row waveform arrays as in-phase channels, and even rows as out-of-phase channels. The in-phase channel is kept fixed; the out-of-phase channel is tilted so that its true angle to the in-phase channel is user-specified.
For control channel pair number n, occupying rows 2n-1 and 2n of the waveform array, the distorted rows are obtained as x_new=x+cos(a)*y and y_new=sin(a)*y, where a is the angle specified for that pair. An angle of 90 degrees therefore leaves the waveform unchanged. A scalar angle specification is expanded to all channel pairs. When a second output is requested, the per-channel mixing matrix is assembled as a sparse matrix holding 1, cos(a) and sin(a) at the (x,x), (x,y) and (y,y) positions of each pair, and the Jacobian with respect to the column-wise vectorisations of the input and the output arrays is the Kronecker product of a unit matrix of the size of the time grid with that mixing matrix. The Jacobian is not built when only one output is requested.
Syntax
[w,J]=non_orth(w,xy_ang)
Parameters
w - waveform, one time slice per column, and
rows arranged as XYXY... with respect to
in-phase and quadrature parts on each
control channel
xy_ang - true angle, in degrees, between the instru-
ment output directions of each X,Y control
pair; may be a scalar or one value per pair,
with 90 degrees corresponding to no distortion
Outputs
w - distorted waveform, same dimension as the
input waveform
J - Jacobian matrix with respect to vectorisa-
tions of the output and the input arrays
Notes
The waveform must have an even number of rows, and the angles must be strictly between 0 and 180 degrees; the transformation becomes singular at both ends of that interval, where sin(a) vanishes and the two output directions become collinear.
See also
no_dist.m, amp_root.m, amp_tanh.m, spf.m, szf.m, restrans.m, transfermat.m, Optimal control module
Version 2.13, authors: Ilya Kuprov
