With the vast array of micro controllers out there and even different levels of arduinos providing more power than the last, is there a mathematical way or some way of knowing how much processing power you need, just by analysis, to run your program as designed in order to choose the right micro?.
Without just trial and error. i.e without just trying it and if it is too slow buying the next chip up.
I've had to do performance projections for computer systems that did not exist yet. Things like cycle time ratios can only give a very rough guide. Generally, I had to resort to simulation, the nearest I could get to measuring on actual hardware.
That said, you may be able to find numbers for benchmarks similar to your code that will at least give you a starting point.
I would not do it by working up one chip at a time - your code may have a problem that makes it too slow for any feasible chip. I would try to find a chip that is fast enough, and work down if it is much faster than needed.
