65 lines
2.0 KiB
TeX
65 lines
2.0 KiB
TeX
\documentclass[addpoints,11pt]{exam}
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\usepackage{url}
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\usepackage{color}
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\usepackage{hyperref}
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\pagestyle{headandfoot}
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\runningheadrule
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\firstpageheadrule
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\firstpageheader{Scientific Computing}{Project Assignment}{WS 2016/17}
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%\runningheader{Homework 01}{Page \thepage\ of \numpages}{23. October 2014}
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\firstpagefooter{}{}{{\bf Supervisor:} Jan Grewe}
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\runningfooter{}{}{}
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\pointsinmargin
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\bracketedpoints
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%\printanswers
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%\shadedsolutions
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\begin{document}
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%%%%%%%%%%%%%%%%%%%%% Submission instructions %%%%%%%%%%%%%%%%%%%%%%%%%
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\sffamily
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% \begin{flushright}
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% \gradetable[h][questions]
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% \end{flushright}
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\begin{center}
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\input{../disclaimer.tex}
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\end{center}
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%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{questions}
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\question In the data file {\tt EOD\_data.mat} you find a time trace
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and the {\em electric organ discharge (EOD)} of a weakly electric
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fish {\em Apteronotus leptorhynchus}.
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\begin{parts}
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\part Load and plot the data in an appropriate way. Time is in
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seconds and the voltage is in mV/cm.
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\part Fit the following curve to the eod (select a small time
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window, containing only 2 or three electric organ discharges, for
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fitting, not the entire trace) using least squares:
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$$f_{\omega_0,b_0,\varphi_1, ...,\varphi_n}(t) = b_0 +
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\sum_{j=1}^n \alpha_j \cdot \sin(2\pi j\omega_0\cdot t + \varphi_j
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).$$ $\omega_0$ is called {\em fundamental frequency}. The single
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terms $\alpha_j \cdot \sin(2\pi j\omega_0\cdot t + \varphi_j )$
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are called {\em harmonic components}. The variables $\varphi_j$
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are called {\em phases}, the $\alpha_j$ are the amplitudes. For
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the beginning choose $n=3$.
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\part Try different choices of $n$ and see how the fit
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changes. Plot the fits and the original curve for different
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choices of $n$. Also plot the fitting error as a function of
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$n$.
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\part (optional) If you want you can also play the different fits
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and the original as sound.
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\end{parts}
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\end{questions}
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\end{document}
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