fix problems in assignments
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@ -39,14 +39,15 @@
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\part Load and plot the data in an appropriate way. Time is in
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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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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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\part Fit the following curve to the eod (select a small time
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window, a few tens of milliseconds, for fitting, not the entire
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window, containing only 2 or three electric organ discharges, for
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trace) using least squares:
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fitting, not the entire trace) using least squares:
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$$f_{\omega_0,b_0,\varphi_1, ...,\varphi_n}(t) = b_0 +
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$$f_{\omega_0,b_0,\varphi_1, ...,\varphi_n}(t) = b_0 +
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\sum_{j=1}^n \sin(2\pi j\omega_0\cdot t + \varphi_j ).$$
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\sum_{j=1}^n \alpha_j \cdot \sin(2\pi j\omega_0\cdot t + \varphi_j
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$\omega_0$ is called {\em fundamental frequency}. The single terms
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).$$ $\omega_0$ is called {\em fundamental frequency}. The single
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$\sin(2\pi j\omega_0\cdot t + \varphi_j )$ are called {\em
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terms $\alpha_j \cdot \sin(2\pi j\omega_0\cdot t + \varphi_j )$
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harmonic components}. The variables $\varphi_j$ are called {\em
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are called {\em harmonic components}. The variables $\varphi_j$
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phases}. For the beginning choose $n=3$.
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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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\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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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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choices of $n$. Also plot the fitting error as a function of
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@ -51,6 +51,8 @@ reconstruct the stimulus a neuron has been stimulated with.
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data.
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data.
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\begin{parts}
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\begin{parts}
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\part Estimate the STA and plot it.
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\part Estimate the STA and plot it.
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\part Implement a function that does the reconstruction of the
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stimulus using the STA.
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\part Implement a function that estimates the reconstruction
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\part Implement a function that estimates the reconstruction
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error using the mean-square-error and express it relative to the
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error using the mean-square-error and express it relative to the
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variance of the original stimulus.
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variance of the original stimulus.
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