QUOTE(jbrohan @ Jan 29 2008, 03:06 PM)
If you have an 8th-degree polynomial fit, why not do a 2nd derivative on the algebraic solution? It all depends on how good is the fit compared to original signal, but algebraic solution wouldn't have bumps...
y = ax^8 + bx^7 + cx^6 + dx^5 + ex^4 + fx^3 + gx^2 + hx + i
dy/dx = 8ax^7 + 7bx^6 + 6cx^5 + 5dx^4 + 4ex^3 + 3fx^2 + 2gx + h
d(dy)/dx^2 = 56ax^6 + 42bx^5 + 30cx^4 + 20dx^3 + 12ex^2 + 6fx + 2g
Use an algorithm to find the zeroes of your second derivative (inflection points), then keep only those values whose first derivatives are positive. (i.e. where the slope stops increasing and starts decreading). After finding "x", the slope can be found by solving dy/dx for this value...
Hope this helps!