John, from the CA3 page (http://www.ebikes.ca/product-info/cycle-analyst-3.html)
Fast Rate: This is an additional fast ramp-up rate for the throttle output that applies only if the CA has not detected any current flow from the battery. It allows the CA’s output quickly reach a level that starts having an effect on the controller before then dropping to the normal ‘up rate’ limit. This eliminates the lag time for a ramped throttle output to catch up with the bike when you apply the throttle and are already moving. Values of 4-8 V/sec are recommended.
Fast Thrsh: This sets the threshold current that must be seen by the CA for it to switch from the “Fast Rate” to the standard ramp-up rate. For direct drive hub motors, it should be quite low, like 0.5 to 1A. But for geared motors or mid-drive systems, it should be higher than the no-load current required to accelerate the motor from still. Usually a threshold of 2 to 4 Amps works well.
My understanding is that - when in motion - these settings tell the motor the rate to spin up until its rpms align with your forward motion. When your no-load spinup (because you're moving) hits the load that you've set in Thrsh, it will switch from 'fast rate' to the normal 'up rate'.
This is strictly to spin up the motor during motion. Otherwise when you're doing 50kmh and you release and reengage throttle, it would lag as it would ramp up at your 'up rate'.
You don't want the thrsh so low that you lag on accel and you also don't want it set too high that it torque-out your chainring