I'm trying to understand a variant of the filter presented in http://www.stockspotter.com/files/PredictiveIndicators.pdf in the "Code Listing 1.". Its expression is given as follow:
$$y_n = c_0 x_n + c_1 y_{n-1} + c_{2} y_{n-2}$$ with:
\begin{align} c_0&=(1-c_1-c_2) \\ c_1&=2 a \cos\left(2\frac{\pi\sqrt{2}}{T_s}\right) \\ c_2&=-a^2 \end{align}
and:
\begin{align} a&=\exp\left({-\frac{\pi\sqrt{2}}{T_s}}\right) \\ T_s&=10 \end{align}
I'm wondering how these coefficients were computed. I'm told it might be a 2-pole Butterworth filter, but my attempts at finding the coefficients for such a filter failed (and my searches online give me many different results, sometimes involving $x_{n-1}$ and $x_{n-2}$ whereas they are not used in this expression.
Does this ``SuperSmoother'' filter has another name in the literature ? How could I describe the effect of such a filter (beside being a low-pass filter)?
The paper is cited in the Linux Kernel's packet rate estimation smoothing.
For the records, here is the response of this filter using the notebook provided in the answers, compared with a moving average and an exponential moving average:
As someone remarked on IRC, this filter looks a lot like the "multiple feedback digital low-pass filter" from Chamberlin 1987 book "Musical Applications of Microprocessors", with $F=\frac{\sqrt{2}}{16}$ and $Q=1$: