Digital filter performance with noncontinuous signal? First of all, I'm new to DSP so excuse my simplified words.
I'm testing the performance of a digital filter on a (partly) noncontinuous signal:



As you can see, the signal is not continuous at some points (like it is stopping and starting over again) When I apply the digital filter to it, I get this:



The filter shows ripples at the noncontinuous areas, then it starts to work again. Why does the filter show this ripple at the noncontinuous areas? How do I calculate it (to know the overshoot, etc.)?
It is not surprising that the filter output resembles the filter's step response at discontinuities of the input signal. It's like applying a (modulated) step at the input. Apparently the cut-off frequency of the high-pass filter is higher than the frequency of the sinusoid, so the output goes to zero after each discontinuity. However, at each point of a discontinuity, the input signal contains frequencies above the cut-off frequency of the high-pass filter and these frequencies are passed to the output.