This is indeed an excellent way of filtering if your audio is cyclic and fits into a single FFT, like a periodic waveform, a drum loop or an Optigan track. Just make sure not to apply any window.
You also need to make sure that the gibbs phenomena does not cause the filtered signal to leave the range of the representation. So a prefiltered signal is less than 1, but the post filtered signal wont be. Meaning if 1 is the cap for your audio output, then enjoy a brand new category of distortion. But its a terrible way in general ofc, just optimize an appropriate, zero phase filter with an unaffected passband and minimum distortion. Its trivially easy, and there is no excuse to just use the terribly shitty short "classic" filters common in audio processing or graphics as implemented by skilled programmers who dont know the difference between dft and fft. (which is always easy to tell as they use the term fft as if it was synonymous with frequency transform estimates)
This is the case for any sharp filter. It is not unique to the FFT approach. It doesn't matter if you use a linear phase FIR; any time you "remove" frequencies you can increase your peak levels. Try graphing sin(x) + 0.2sin(3x) and then try removing/filtering out the 3x component.
It's even true for reconstruction. A digital waveform can represent peak levels far above "digital peak", in between samples.
This is why if you're mastering songs, you'd better keep your peak levels at -0.5dB or -1dB so (so the filtering from lossy compression won't make it clip), and why you'd better use an oversampling limiter. Especially if you're doing loudness war style brutal limiting, because that's the stuff that really creates inter sample peaks. But you shouldn't be doing that, because Spotify and YouTube will just turn your song down to -14 LUFS anyway and all you'll have accomplished is making it sound shitty :-)
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.
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.
Modern computers are ridiculously powerful, processing a 4k image with a 50x50 filter is real time >60hz on cpu using a decent fft solution, and on a decent gpu you could do many times more >60hz.
Oh sure, there are lots of usecases for fast but bad. But what bugs me is that people arent using them for those cases. Worse still, people are using repeated fast but bad, and then more fast and bad to fix the problems that caused, and effectively creating slow and bad filters.