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[project_eod] textual changes

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Jan Grewe 2019-01-10 17:39:18 +01:00
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projects/project_eod/eod.tex
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@ -11,30 +11,37 @@
%%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%% Questions %%%%%%%%%%%%%%%%%%%%%%%%%
Weakly electric fish employ their self-generated electric field for
prey-capture, navigation and also communication. In many of these fish
the {\em electric organ discharge} (EOD) is well described by a
combination of a sine-wave and a few of its harmonics (integer
multiples of the fundamental frequency).
\begin{questions} \begin{questions}
\question In the data file {\tt EOD\_data.mat} you find a time trace \question In the data file {\tt EOD\_data.mat} you find two
and the {\em electric organ discharge (EOD)} of a weakly electric variables. The first contains the time at which the EOD was sampled
fish {\em Apteronotus leptorhynchus}. and the second the acutal EOD recording of a weakly electric fisch
of the species {\em Apteronotus leptorhynchus}.
\begin{parts} \begin{parts}
\part Load and plot the data in an appropriate way. Time is in \part Load the data and create a plot showing the data. Time is given in
seconds and the voltage is in mV/cm. seconds and the voltage is given in mV/cm.
\part Fit the following curve to the eod (select a small time \part Fit the following curve to the EOD (select a \textbf{small} time
window, containing only 2 or three electric organ discharges, for window, containing only two or three electric organ discharges, for
fitting, not the entire trace) using least squares: fitting, not the entire trace) using least squares:
$$f_{\omega_0,b_0,\varphi_1, ...,\varphi_n}(t) = b_0 + $$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 \sum_{j=1}^n \alpha_j \cdot \sin(2\pi j\omega_0\cdot t + \varphi_j
).$$ $\omega_0$ is called {\em fundamental frequency}. The single ).$$ $\omega_0$ is called the {\em fundamental frequency}. The single
terms $\alpha_j \cdot \sin(2\pi j\omega_0\cdot t + \varphi_j )$ 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 the {\em harmonic components}. The variables $\varphi_j$
are called {\em phases}, the $\alpha_j$ are the amplitudes. For are called {\em phases}, the $\alpha_j$ are the amplitudes. For
the beginning choose $n=3$. the beginning choose $n=3$.
\part Try different choices of $n$ and see how the fit \part Try different choices of $n$ and see how the fit
changes. Plot the fits and the original curve for different changes. Plot the fits and the section of the original curve that
choices of $n$. Also plot the fitting error as a function of you used for fitting for different choices of $n$. Also plot the
$n$. fitting error as a function of $n$.
\part Why does the fitting fail when you try to fit the entire recording?
\part (optional) If you want you can also play the different fits \part (optional) If you want you can also play the different fits
and the original as sound. and the original as sound (check the help).
\end{parts} \end{parts}
\end{questions} \end{questions}