The ac-coupling of an oscilloscope is not a filter a "0" Hz. It is normally just a simple capacitance that, with the 1MOhm input impedance of the oscilloscope, acts like a first order high-pass filter with a cut-off frequency of few hertz.
Try to implement a highpass Butterworth filter of order 1 and with a low cut-off frequency of 10 Hz.
You can then play with the cut-off frequency and see which value works best for you (remember to connect the right value to the sample frequency input of your filter). You can also try to increase the filter order to 2 (some measurement devices have input high-pass filters of order 2 or even 3).