About a filter's rise time I have just a few questions regarding the rise time of filters.

A rise time seems to be measured by using a step input, with an input typically from 0 to 1. However this is what I cannot seem to find out...

-Does the rise time stay the same if input is from say 0 to 0.5 or some other arbitrary input?

-If not, how can I predict the rise time?

-If so, what happens if I input 0 to 0.5, hold at 0.5, and then step to 1? Does another rise time occur?

Thanks for any information!
When a system is linear, effects are proportional to causes. You can multiply the input by any constant, you'll get the same output multiplied by the same constant.

If you look at how the rise time is defined, you'll see that it is independent of any amplification factor.

You can also add two inputs, and the output will be the sum of the separate outputs corresponding to the separate inputs.

So it you apply a second, delayed step, there can be two situations


steady state (constant output) has been reached after the first step: then you can consider two distinct rises with equal times;
steady state has not been reached yet: there is a single, combined rise, with a different rise time.