Recalling the basic generating equations
X-axis
x(t) = A sin nwt cos wt
Y-Axis
y(t) = A sin nwt sin wt
The components forming the circular portion are
cos wt for X-axis
and
sin wt for Y-axis
The perturbations are due to
sin nwt, both axes
If the correlation sensed during each rosette petal is detected
and smoothed, a resulting function of the form G(9) cos (wt + 0) is ob
tained. This is a modulated sinusoid whose phase angle with the rosette
X-axis circular sweep signal term, cos wt, is the angle formed by the con
tour and the rosette deflection axis . The quantity G(9) is an amplitude
term related to the steepness of the local slope. (Since orthogonal cor
relation is being used, G(9) is maximum when the degree of correlation
is minimum.) The required forcing voltages for both axes may be obtained
by considering the phase of the correlator output function as compared to
the phase of the low-frequency rosette generating signals. Allowing the
correlator output function to have a normalized gain, A, then
G(9) cos (wt + 0) ^ A cos (wt + 0)
where
The X-axis steering signal is obtained from the product
E {0) = A^ cos wt cos (wt + 0)
E x ( ^ " 4p- cos 0 + ^— cos (2 wt + 0)
cos [0) - cos (-0)
Also for Y-axis:
E {0) = A^ sin wt cos (wt + 0)
^ 2 2
Ey(0) = - sin 0 + — sin (2 wt + 0)
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