Why does applying a high‑pass filter to a sound sometimes result in the output being noticeably higher than it was before? Today I have been working on a sound that peaks at 0dBFS. It has a lot of low‑frequency content. I am applying a high‑pass filter at around 100Hz and the output from the EQ is peaking at around +4dBFS. Why should this happen? Most of the power in this sound is in the low frequencies, and it has little going on above 2kHz, so surely with the high‑pass filter most of the energy from the sound has gone!
Via SOS web site
SOS Technical Editor Hugh Robjohns replies: This is a very common effect and there are several possible reasons for it. Fundamentally, the filtering process changes the shape of the waveform, so although there may be less total energy in the signal, the peak amplitude may well increase.
If you think about a bunch of different‑frequency tones all playing at the same time, their phase relationships vary continuously and add to or cancel each other to create the total waveform. Remove some of those tones and some of those cancellations won't occur. That can result in the waveform becoming bigger. 
There are various reasons why using a high-pass filter on a signal can make it sound louder. Some equalisers, for example, actually boost the region just above the turnover frequency, which can produce an increase in peak level.
Most equalisers also introduce significant phase shifts and that, again, will change the way different frequencies combine and cancel. It can also happen because some equalisers actually boost the region just above the turnover point below which they are attenuating, potentially increasing peak level.