I recently implemented a Butterworth high-pass filter (2nd order). Everything seems to work fine, except that I have a question when applying such a filter to a constant signal. As there are no high-frequency components in a constant signal, I would expect the filter to yield a constant 0 signal.
In the plots below are my results. There seems to be ``ripple'' in the first couple of frames before the high-pass filtered signal (correctly) converges to 0.
Is this a logical result from applying a Butterworth high-pass filter on a constant signal, or might there be a bug in my code?
EDIT: I've created the same filter in Octave, resulting in the same output. This indicates that we're indeed looking at the step response, as Paul R. indicates.