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Signed-off-by: David Rotermund <54365609+davrot@users.noreply.github.com>
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@ -472,7 +472,7 @@ $$\sigma_{a_1} = \sqrt{\frac{\Sigma_{x^2}}{\Sigma\Sigma_{x^2}-(\Sigma_x)^2}} , \
As an example we consider:
$$\hat{x}_k = \frac{1}{2\pi} \int_{0}^{2\pi} x(t') \exp\left( -ikt' \right) \, dt' \approx frac{1}{2\pi} \sum_{n=0}^{N-1} a_n \exp\left( -ik 2\pi t_n/T \right) \Delta t'$$
$$\hat{x}_k = \frac{1}{2\pi} \int_{0}^{2\pi} x(t') \exp\left( -ikt' \right) dt' \approx frac{1}{2\pi} \sum_{n=0}^{N-1} a_n \exp\left( -ik 2\pi t_n/T \right) \Delta t'$$
Here the fit parameters are $a_1 = 0.1529 \pm 0.2633$ and $a_2 = 1.0939\pm 0.0670$. Note that the error bars $\sigma_{a_j}$ do not depend on the $y_i$. These error bars are thus no quantifier of the goodness of the fit.