30.1.52 ExpDec3

Function

$y=y_0+A_1e^{-x/t_1}+A_2e^{-x/t_2}+A_3e^{-x/t_3}$

Three-phase exponential decay function with time constant parameters.

Number: 7

Names: y0, A1, t1, A2, t2, A3, t3

Meanings: y0 = offset, A1 = amplitude, t1 = time constant, A2 = amplitude, t2 = time constant, A3 = amplitude, t3 = time constant

Lower Bounds: none

Upper Bounds: none

Note: different initial parameters are used for t1, t2 and t3 so as to make sure t3 > t2 > t1 in the fitting results.

Individual decay rate:

k1=1/t1

k2=1/t2

k3=1/t3

Individual half life:

thalf1=t1*ln(2)

thalf2=t2*ln(2)

thalf3=t3*ln(2)

Note: Half life is usually denoted by the symbol $t_{1/2}$ by convention.

nlf_expdec3(x,y0,A1,t1,A2,t2,A3,t3)

FITFUNC\EXPDEC3.FDF