Crescendo, in one sense, may be viewed as a complex process. To me, having worked on it for the past two decades, it seems entirely sensible. But whenever I have to explain it to others, we often get mired in complex terminology and math.
I just ran across the PhD Thesis of Michael Mark Goodwin, from MIT, back in 1992, entitled Adaptive Signal Models: Theory, Algorithms, and Audio Applications. This is a very exciting discovery because, in that thesis, he provides a very good mathematical explanation for exactly what my Crescendo algorithm is actually doing.
In particular, if you want to understand the basis of Crescendo, you should focus on his Chapter 4, on Residual Modeling, where he discusses the use of nonuniform filter banks, noise power estimation, and perceptual accuracy.
While Goodwin is more concerned with signal analysis and re-synthesis from compact representations of audio signals, our Crescendo exactly parallels his analysis stages but applies its results to the expression of pass-through gains on an original audio signal. We are not re-synthesizing anything in Crescendo, just modifying the spectral gains of the original signal according to a recruitment compensating compression gain in each perceptual critical band.
Our EarSpring and Conductor papers focus on the nature of recruitment compensation within any one critical band. Goodwin provides the explanation for how we apply those findings to all critical bands across the audible spectral range.
Goodwin’s explanations are the most precise and succinct descriptions of our Crescendo process that I have ever seen, including all of my past attempts.
It is also gratifying that he provides a mathematical proof that we are doing the correct thing in Crescendo. Of course, our ears already tell us that…
- DM
