[vamfun]

Originally Posted by Alan Anderson

I have no idea what you're trying to say here.

Here is pseudo simulation code that I would write to illustrate the error amplification

Param: 
T = edge oscillation period
A  = edge oscillation amplitude
dt = T/20,  sample rate small enough to measure oscillation
variables: 
t = time,
x = encoder input
y = encoder output
x_dot = encoder input rate 
y_dot= encoder output rate

Run Simulation:
while(t < runtime){

Encoder input movement:

x = A*sin(2*pi*t/T); Small oscillation movement , A < 1 to be on same edge.

x_dot = A*2*pi/T*cos(2*pi*t/T)

Encoder output change when x is centered on a threshold:

If(x > 0 ) {y = .5 }   //sample
else {y = -.5 }

y_dot = (y-y_last)/dt   //Derive simple rate 
y_last = y;
t= t + dt;
}

Expected Results:
The output amplitude will oscillate between -.5 and .5

The amplitude ratio y/x = .5/A.

peak |y_dot| = 1/dt,

average |y_dot| = 2/dt/(20)= 2/T Average over oscillation period



Then (avg |y_dot|)/(x_dot amplitude) = 1/(A*pi)
(this is slightly less than my .5/A approximation.)