Testing:

We move a logic output every x ms connected to an analog input. The input signal is square. The climb has a slight rounding at the end of 50 micro sec. There are no visible imperfections in the descent.
When the output goes to zero, at each lap of the cycle, we record the analog value in an array of 100.
We also calculate the average cycle time over 10 seconds.

The results are in the following table:

It takes about 20 ms for the read value to pass from max to min (15 ms to pass from low signal: 0.7 volt to high signal: 3.3 volts). And vice versa.
If we make a 10 volt slot, we’ll probably get close to 50 ms.
Sampling of an analog input with this test program: 342 μs (Cycle time)