f(x)=exp(x/x0)*(a*cos(2*pi*x*f)+b*sin(2*pi*x*f))

a=.4
b=.3
f=1.5
x0=20

fit [-40:-5] f(x) 'raw_data_files/C2optspect20110120-100001.txt' every ::6 using ($1*1E9-5500):2 '%lf,%lf' via a,b,x0,f


set samples 2000


plot [-80:20] [:] 'raw_data_files/C2optspect20110120-100001.txt' every ::6 using ($1*1E9-5500):2 '%lf,%lf' w l, f(x)

# result:
Final set of parameters            Asymptotic Standard Error
=======================            ==========================

a               = 0.138361         +/- 0.003389     (2.45%)
b               = -0.460588        +/- 0.003238     (0.7031%)
x0              = 17.4024          +/- 0.1403       (0.8061%)
f               = 1.50056          +/- 7.423e-05    (0.004947%)


correlation matrix of the fit parameters:

               a      b      x0     f
a               1.000
b              -0.041  1.000
x0             -0.376  0.805  1.000
f              -0.847 -0.192  0.163  1.000