## High-End Hysteresis

I decided to try an experiment, after several months of critical listening with multi-channel noise gating. I noticed that with extreme levels of hearing correction applied, there were quite often noise artifacts included in the playback, at the highest frequencies. Crescendo was trying too hard to let me hear absolutely everything.

But most recordings carry noise, especially dominant at the very highest frequencies. And those portions of the signal are just noise. Recording studios often make use of noise gates on their microphones to avoid picking up room noises. So I tried adding a little bit of gating at the highest octaves above 4 kHz, and it helped considerably.

Crescendo already had a form of noise gating in that it wouldn’t (A) perform more than some considerable amount of gain in the quietest channels – with dynamics protection, and (B) when the signal dropped below 30 dBSPL, it would gradually reduce the applied gain, making it seem, with impaired hearing, that the signal had dropped significantly more. But still, some noise managed to make its way through.

Noise follows a roughly Gaussian distribution, which means that even when we really have no signal, the additive noise can rise above the noise floor, making Crescendo think that there is some signal there. Most often, the additive noise is small, and that leads Crescendo to produce a crunchy sort of sound, as the levels go from no assist, to considerable assist, and then back in the next instant. That was the noise I wanted to remove.

Hysteresis sets one threshold for realizing that we have reached the noise floor (30 dBSPL = a quiet, empty, auditorium), while using a second threshold to realize when there really is some signal.

With Gaussian statistics, a good measure of actual signal being present is when its level + noise rises by 10 db above the noise floor. That corresponds to a 3-sigma event in statistics, which is a 1 in 600 chance of just randomly happening.

Experimental physics likes 5-sigma events to make us believe that some effect actually happened. But we will use 3-sigma. Any random event that is 3-sigma or more will be rare, and weak. We end up removing 99.9% of all the crunchies, which is a substantial improvement.

Here is a graph showing a hypothetical signal + noise profile in the music in one channel at the highest frequencies. It starts out at a level of 70 dBSPL (pretty loud), and then decays down to the noise floor at 30 dBSPL. The noise in the system has a constant level, but in a dB plot it is hardly visible at the loudest levels and only starts showing up as we decline toward the noise floor.

Then, it rises in a crescendo to 50 dBSPL and decays away again.

The red curves show the applied Crescendo gains for a hearing threshold elevation of 70 dB (pretty severe). You see how it immediately ceases working once the signal falls below the 30 dBSPL noise floor. And with hysteresis it doesn’t come back on until something really is there.

Without hysteresis, anytime the signal pops up above the noise floor, Crescendo would go into action with a controlled gain increase, using a 10 ms time constant. And so with all that hair on the noise floor, we would be popping on and off quite a lot – which generates crunchy noise in the highest frequencies.

Because of the 10 ms smoothing, it didn’t sound as bad as it could have with a hair trigger. But crunchies still made their way through. That 10 ms smoothing is apparent in the curvature of the red curves as the signal rises or falls in a straight line dB manner.

With hysteresis and a 10 dB margin, Crescendo now only turns back on when there seems to be a real signal there. You might miss the very beginning instant of a sound, but these are very weak sounds, and if there is really something there, it is most likely because something at a lower frequency is becoming even louder, and that draws your attention.

But the good thing about this mechanism is that Crescendo now remains active on the way back down, all the way until the signal once again crosses the noise floor. Hence you get to hear the whole reverb tail, which is the most important part of a decaying sound.

Turns out, this works really well, and I can dispense with the multi-channel noise gating. Crescendo now has that built into every one of its 100 channels – a far more precise instrument than a 4-band multi-channel noise gate.

• DM