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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