What is really meant by pulse distortion? I have come across several paragraphs which mentions the cause of the pulse distortion is group delay. But doesn't a LP filter still distort a pulse even though the filter would have a constant group delay? I mean a LP filter attenuates the amplitude of an input differently at different frequencies. A pulse would be composed of superimposed sinusoids at different frequencies and each sine component of the pulse will be attenuated differently by the filter. Wouldn't that cause a distortion as well?
I ask this because the sources I come across never mentions this and relate the distortion only to the group delay. So I suspect maybe I don't know the true definition of pulse distortion. Would you call a pulse distorted if it is filtered by a LP filter with a constant group delay?