Yes and other IC can sort of do that, even if the driver manufacturer use support components to set a fixed value for that. For example Mr Nophead has a post here on the topic, in a case like that imagine that resistor would of been a pot instead, it would give the user an additional ability to tweak the driver to the motor.
The step command has nothing to do with the frequency at which the step command is issued. The uC can issue step commands at any frequency, and that relates to the speed at which the motor is supposed to move. When the driver sees a step (e.g. step function, rise edge), the driver understands to make a move. Thats all. What move that is, depends on the microstep regime, but its still only one move.
The step function in signal class means only a move from 0 to 1, only this part is a function named step. After this, how long the signal stays at 1, or how it decays, this does not matter. Only the rising part from 0 to 1 matters, that is the step function as in the theory book. There are a few basic signals from which all other signals can be constructed, step is one of those, an elementary function of time in signal theory. Some drivers will monitor the line after step, to be high for some time, e.g. step width to have a minimum time as value 1, but that is for the purpose of filtering out false rising signals like wires cross-talk and such. If the exact width of the 1-value after the step would have a meaning like velocity or acceleration, that would be a DC servo driver. If the frequency of the step itself would have some meaning as in position, then it would be sort of an RC servo. Our stepper drivers only understand the step function, verifies it a little to make sure it was valid, but thats all. And each step is only 1 move, be it full step or ustep. Besides this, the driver does not interpret the frequency or length of any other parts. So it is not a pulse (pulse is an area), its just a step, and step is just a line, vertical, where value jumps from 0 to 1 (or if it jumps down its the inverse function of step).
So the step frequency basically has nothing to do with anything that happens internally with the coils of the motors. The step frequency itself is not interpreted (not like RC servo). Only each individual steps are interpreted, and independent from each other, and each mean just one thing, make 1 move. The frequency at which the motor coil work, the chopping frequency, that is something internal to the stepper driver instead. For example if the motor stays still, there is (was) no step command issued. But the coil still work at some frequency that is, so you can see these are not linked.
So there is an on-time, rise time, characterized by the e^(-t/tau), because it is a "natural" rise. But the fall time is not characterized by that, because its is mostly not natural: chip can have synchronous rectification inside, sort of meaning that when the time comes it will put the coils ends on short circuit like a recirculation diode, so the current will keep running in circles inside the coil until it dissipates. Or can have 8 external diodes, which again have an impact this way. Anyway, the off-time is not entirely a "natural" falling edge hence not with e^(-t/tau). The "off-time" might have separate intervals, e.g. differently there might be a "blank" time which is basically a wait time when internal comparators are disabled for the purpose of not getting annoying values over Rs (hence false readings) caused by coil inductive spikes. So while not mixing the datasheet off-time with other things, lets call our "off-time" with respect to voltage being applied to the coil, so that would be perhaps better for our purpose, at least is more clear. So we take it as an on-time and off-time and thats basically everything there is. Then i think computing average resembles much with a buck regulator where D is on-time and (1-D) is off-time. Except our (1-D) is not natural, because we actively force current to decay or else we want to put it down to ground, instead of just "naturally" letting it out by itself.
The step command has nothing to do with the frequency at which the step command is issued. The uC can issue step commands at any frequency, and that relates to the speed at which the motor is supposed to move. When the driver sees a step (e.g. step function, rise edge), the driver understands to make a move. Thats all. What move that is, depends on the microstep regime, but its still only one move.
The step function in signal class means only a move from 0 to 1, only this part is a function named step. After this, how long the signal stays at 1, or how it decays, this does not matter. Only the rising part from 0 to 1 matters, that is the step function as in the theory book. There are a few basic signals from which all other signals can be constructed, step is one of those, an elementary function of time in signal theory. Some drivers will monitor the line after step, to be high for some time, e.g. step width to have a minimum time as value 1, but that is for the purpose of filtering out false rising signals like wires cross-talk and such. If the exact width of the 1-value after the step would have a meaning like velocity or acceleration, that would be a DC servo driver. If the frequency of the step itself would have some meaning as in position, then it would be sort of an RC servo. Our stepper drivers only understand the step function, verifies it a little to make sure it was valid, but thats all. And each step is only 1 move, be it full step or ustep. Besides this, the driver does not interpret the frequency or length of any other parts. So it is not a pulse (pulse is an area), its just a step, and step is just a line, vertical, where value jumps from 0 to 1 (or if it jumps down its the inverse function of step).
So the step frequency basically has nothing to do with anything that happens internally with the coils of the motors. The step frequency itself is not interpreted (not like RC servo). Only each individual steps are interpreted, and independent from each other, and each mean just one thing, make 1 move. The frequency at which the motor coil work, the chopping frequency, that is something internal to the stepper driver instead. For example if the motor stays still, there is (was) no step command issued. But the coil still work at some frequency that is, so you can see these are not linked.
So there is an on-time, rise time, characterized by the e^(-t/tau), because it is a "natural" rise. But the fall time is not characterized by that, because its is mostly not natural: chip can have synchronous rectification inside, sort of meaning that when the time comes it will put the coils ends on short circuit like a recirculation diode, so the current will keep running in circles inside the coil until it dissipates. Or can have 8 external diodes, which again have an impact this way. Anyway, the off-time is not entirely a "natural" falling edge hence not with e^(-t/tau). The "off-time" might have separate intervals, e.g. differently there might be a "blank" time which is basically a wait time when internal comparators are disabled for the purpose of not getting annoying values over Rs (hence false readings) caused by coil inductive spikes. So while not mixing the datasheet off-time with other things, lets call our "off-time" with respect to voltage being applied to the coil, so that would be perhaps better for our purpose, at least is more clear. So we take it as an on-time and off-time and thats basically everything there is. Then i think computing average resembles much with a buck regulator where D is on-time and (1-D) is off-time. Except our (1-D) is not natural, because we actively force current to decay or else we want to put it down to ground, instead of just "naturally" letting it out by itself.