For testing the alternator you will probably have an easier job if you use PicoDiagnostics and use the battery test option. This will test the battery, alternator and starter motor in one go.https://www.picoauto.com/pico-diagnostics.html
For your waveform you have got some fairly large spikes so it might be worth checking you have a good ground connection and the wires are well away from injectors and ignition components. The spikes however are not from the alternator so as you suggest can be filtered out - try a 10kHz filter on channel A.
Channel A in your test is AC coupled so shows the alternator does not have any blown diodes. Channel B shows a current of about 25A. If the engine was running and this is a charging current then again this may be OK.
I suggest you next either use PicoDiagnostics or use the preset for testing Current / Volts / Starting (12V). This will show the battery DC voltage before, during and after starting. It will also show the peak current draw. Once you have saved this test it might also be worth keeping the same settings, switch off the car and capture again with a much longer timebase - say 200 sec/div so you can see if anything is still drawing current after the engine has been switched off.
With this waveform and the one you have captured we should have a clear idea of the problem.