47 lines
1.6 KiB
TeX
47 lines
1.6 KiB
TeX
\documentclass[a4paper,12pt,pdftex]{exam}
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\newcommand{\ptitle}{EOD waveform}
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\input{../header.tex}
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\firstpagefooter{Supervisor: Jan Grewe}{phone: 29 74588}%
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{email: jan.grewe@uni-tuebingen.de}
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\begin{document}
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\input{../instructions.tex}
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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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