I'm with Si.
There is no need to over complicate this.
All you need is enough accuracy & precision to be able to distinguish between the coins.
Notice that the induction is influencing the roll speed between the different coins
by more than a 100ms time difference between the coins.
That is all day long to the AVR.
Plus it does not require super precise timings in order to be able to distinguish
between the coins.
Based on a known timing range for the coins, you can figure out which coin it is.
i.e. don't look for an exact timing value of an individual coin, look for > or < some other number
relative to the other coins.
You can nest your comparisons so that you only compare to one timing value
for each coin.
In his case:
if ( dt > 1000) quarter
else if( dt > 900) dime
else if(dt > 700) penny
else nickel
You will probably have to experiment a bit to determine what times identify each coin
and potentially tune your detector by varying a a few things like the slope of the
ramp to control the entry speed into the magnetic field and the strength of the field
by varying the distance between the coin and magnets.
--- bill