[marcan_42]

You didn't understand my example. This isn't about spectral ringing. It doesn't matter if you have zero spectral ringing, and no amplitudes above 1. There is no way to have a sharp filter that removes (or almost removes) certain frequencies, even if it has zero spectral ringing, while guaranteeing it doesn't increase peak levels in the time domain. The filter will decrease the total energy of the signal, but a decrease in signal energy can still cause an increase in peak levels. This is because the addition of a frequency component can decrease peak levels by lining up with the existing peaks in such a way, and thus removing it can conversely increase peak levels.

Just punch sin(x) + 0.2sin(3x) into a graphing calculator, then remove the 0.2sin(3x) component and look at peak levels increase. No filter can fix that without also decreasing the sin(x) component significantly to compensate.