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\firstpageheader{Scientific Computing}{Project Assignment}{11/02/2015
  -- 11/05/2015}
%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
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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 small time
    window, containing only 2 or three electric organ discharges, for
    fitting, not the entire trace) using least squares:
    $$f_{\omega_0,b_0,\varphi_1, ...,\varphi_n}(t) = b_0 +
    \sum_{j=1}^n \alpha_j \cdot \sin(2\pi j\omega_0\cdot t + \varphi_j
    ).$$ $\omega_0$ is called {\em fundamental frequency}. The single
    terms $\alpha_j \cdot \sin(2\pi j\omega_0\cdot t + \varphi_j )$
    are called {\em harmonic components}. The variables $\varphi_j$
    are called {\em phases}, the $\alpha_j$ are the amplitudes. For
    the beginning choose $n=3$.
    \part Try different choices of $n$ and see how the fit
    changes. Plot the fits and the original curve for different
    choices of $n$. Also plot the fitting error as a function of
    $n$. 
    \part (optional) If you want you can also play the different fits
    and the original as sound.
    
  \end{parts}
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