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\firstpageheader{Scientific Computing}{Project Assignment}{11/05/2014
  -- 11/06/2014}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\begin{questions}
  \question In the data file {\tt EOD\_data.mat} you find a time trace
  and the {\em electric organ discharge (EOD)} of a weakly electric
  fish {\em Apteronotus leptorhynchus}. 
  \begin{parts}
    \part Load and plot the data in an appropriate way. Time is in
    seconds and the voltage is in mV/cm.
    \part Fit the following curve to the eod (select a smaller time
    window for fitting, not the entire trace) using least squares:
    $$f_{\omega_0,b_0,\varphi_1, ...,\varphi_n}(t) = b_0 +
    \sum_{j=1}^n \sin(2\pi j\omega_0\cdot t + \varphi_j ).$$
    $\omega_0$ is called {\em fundamental frequency}. The single terms
    $\sin(2\pi j\omega_0\cdot t + \varphi_j )$ are called {\em
      harmonic components}. The variables $\varphi_j$ are called {\em
      phases}. For the beginning choose $n=3$. 
    \part Play around with $n$ and see how the fit changes. Plot the
    fits and the original curve for different choices of $n$. If you
    want you can also play the different fits and the original as
    sound.
    
  \end{parts}
\end{questions}





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