$$PENDING
for A/D stuff, one can do the following (w/o showing scaling)
1. z transform calculator
2.Bode plot of s/(1-s) sampling period 0.02
3. bode plot of (2 z (2 z+1)) / (2 z-1)^3
One must match the Initial value of the Analog/Digital.
Note the modified z-transform would map roots to [ 1 - A*(4w/ws)^B ] with (A,B) a f{specific system}
As 4*wi approaches Ws, of course we see [1 - A]
z-root: ~ exp(aT) *[1-0.85*(4a/Ws)^3.17 ] ie (a,b) = ( 0.85,3.17 )
recall Ws= 2Pi/T so given t=0.2s, Ws= 31.4. So, for (s +2.5), converts to (z+ 1.61), where the mult adjust= 0.98
If sampling is slowed to say 10 rad/s (T= 1.26s), the mult adjust = 0.15, a substantial decrease from the std z-transform
Recall FVT s*F(s) as s goes to 0 and (z-1)F(z) as z goes to 1
IVT s*F(s) as s goes to infinity and F(z) as z goes to infinity
So, from above FVT analog=0. digital=0. IVT analog -infinity digital =0.5
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