[Scilab-users] Identifying parameters of a multy frequency damped oscillation

[Jens Simon Strom]

Hi Scilab users,
I  want  to  analyse  a  microphone  recording  of  the  sound  of  a  bell  or  gong.Given  ia  the  equidistantly  sampled  sound  pressure  y(t)  after  a  stroke  for  10  s.

The  ansatz  

y=sum(   A_i*exp(-d_i*t))*cos(2*%pi*f_i+alpha_i)   )   for i=1,2,...5 or more

is  assumed  to  approximate  the  signal  where  A_i,  d_i,  f_i,  and  alpha_i  are  the  unknown  amplitudes,  danping  factors,  frequencies,  and  phase  angles  of  y.  The  analysis  may  be  restricted  to  the  lowest  5  frequencies  fi.
Does  Scilab  offer  a  method  for  this?  FFT seems not to be adequate  because  the  signal  is  aperiodic  (silence  after  10  s).
Is  nonlinear  regression  (with whichI'm  fmiliar)  a  promising  way.  The  lowest  frequencies  can  probably  be  concluded  from  a  short  time  DFT  where  damping  is  negligible.
Kind regards
Jens

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