[midjji]

not quite, designing minimum passband distortion filters with no amplitude increase anywhere is slightly harder, but its not impossible. Even if you are strictly removing some specific frequencies, as you can design the filter in such a way that the spectrum amplitude ringing strikes zero for them. In practice though, simply reducing these frequencies by a factor of 100 is good enough and thats possible for bands without needing to have any amplitude above 1.

[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.