diff --git a/projects/project_eod/eod.tex b/projects/project_eod/eod.tex index 647a756..e225546 100644 --- a/projects/project_eod/eod.tex +++ b/projects/project_eod/eod.tex @@ -11,31 +11,38 @@ %%%%%%%%%%%%%% 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} - \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}. + \question In the data file {\tt EOD\_data.mat} you find two + variables. The first contains the time at which the EOD was sampled + and the second the acutal EOD recording of a weakly electric fisch + of the species {\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 + \part Load the data and create a plot showing the data. Time is given in + seconds and the voltage is given in mV/cm. + \part Fit the following curve to the EOD (select a \textbf{small} time + window, containing only two 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 + ).$$ $\omega_0$ is called the {\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 the {\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 - $n$. + changes. Plot the fits and the section of the original curve that + you used for fitting for different choices of $n$. Also plot the + 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 - and the original as sound. - + and the original as sound (check the help). + \end{parts} \end{questions}