How many channels are best for audiology corrections? Are many channels better than fewer channels?
When I began my research, it became pretty clear that simply using FFT channels was a poor design. FFT channels are all equal-width. But as we go to higher frequencies, the music power declines, typically 4-6 dB/octave. And by the time we reach the frequencies most affected by sensioneural hearing impairment, there is so little music power in each FFT cell that our corrections become dominated by noise power. The corrections become too large.
Furthermore, our hearing is “channelized” into critical bands with roughly constant percentage bandwidth – meaning that as we go to higher frequencies those bandwidths grow wider in absolute frequency measure. But these “channels” are not hard-wired into our brains at specific frequencies. Rather, they are self-organizing bands that surround the loudest sounds in the spectrum.
So, back up and use frequency bands whose bandwidths are more closely related to our hearing critical bandwidths. There are 24-25 Bark bandwidths across the audible spectrum from 20 Hz to 20 kHz. Should we use 25 bands? 50 bands, 100 bands? What happens if we group Bark bands together and use even fewer than 25 bands?
My early designs assumed that more is better, and so they tended to be 50 or 100 Bark subbands. My reasoning was that these would be placed at fractional Bark spacings and more accurately pick up on the self-organizing bands that form in our perception. And it sounded pretty good!
But then one day, I decided to try one band per Bark, for 25 bands. And that sounded pretty good too! Better?
Well whether or not a sound seems better is a very difficult thing to measure. Something new always sounds more interesting. So how do you decide whether or not the new interesting sound is better? That is a purely subjective judgement, not amenable to mathematical analysis.
And then one day, I decided to look at even broader bandwidths. First off, in considering possible alternative Crescendo architectures, perhaps using simple IIR filters, it becomes very difficult and prohibitively costly in CPU cycles to support very narrow bandwidths.
Audiology testing frequencies are spaced at half-octave intervals, and are roughly 2.5 Bark apart, ranging over the frequencies 250 Hz, 500 Hz, 750 Hz, 1 kHz, 1.5 kHz, 2 kHz, 3 kHz, 4 kHz, 6 kHz, and 8 kHz. At the very highest frequencies, and beyond, the measurements become very difficult to do properly, and any reported audiology is highly suspect.
But what would happen if I did an architecture for Crescendo based solely on those standard audiology test frequencies? I tried it out, and again it sounded astonishingly good. Very different from the narrow band versions of Crescendo. But better?
Different always sounds better for a while. So my current design that I’m listening to is based on the standard audiology frequency bands. And I will have to live with it for a while before I can actually decide if it is better or not. But it does sound very very good.
Is there, perhaps, some reason that it should sound better with wider bandwidths? Maybe… We know in visual processing that our eyes are most sensitive to spatial intensity variations, but not so sensitive to spatial color variations. That’s why today’s electronic cameras seem to do such a decent job. The color resolution is actually lower than the pixel resolution, due to the almost universal use of Bayer color masks.
Perhaps something similar exists in the auditory processing of our brains? Loudness variations might have less spectral sensitivity than tone pitch variations. It almost certainly does. And my various experiments with ever decreasing numbers of widening bands pretty much shows this. Yet our pitch perception is good to a small fraction of a Bark bandwidth almost everywhere below 4 kHz. Not so much at extremely high frequencies.
At the extremes, I have even done 3 band Crescendo systems. You can easily mock those up with standard audio plugins. And I do have to say that while these 3-band units could be used in an emergency situation, they really don’t sound as good as a real Crescendo. So we know that there is some point where we would have too few bands to sound good.
But I would have to say, based on today’s new version, that the limit for good sound quality must be at or fewer than 10 bands at the standard half-octave frequencies. And it is possible that using too many bands damages the quality of sound corrections. Perhaps there is some optimum number of bands across the audio spectrum?