Hi,
I am adding strong noise which has zero mean to an OOK modulation. I use for that the matlab function 'randn'. But after this, I apply a chebyshev 3º order bandpass filter and I don't really know if the output signal would have the same property of zero mean or not?
If the input noise for the BPF has long term zero mean, the output will also have long term zero mean (that means there is no DC component). If the BPF has low BW/fc ratio, the noise looks like a modulated sinusoidal function (it has both amplitude and phase modulation).