Decompositions of Natural Signals Still Need Fresh Ideas

Опубликовано 22 июня 2016, 2:22

…musical tones are the simpler and more regular elements of the sensations of hearing, and that we have consequently first to study the laws and peculiarities of this class of sensations. Hermann von Helmholtz, On the Sensations of Tone as a Physiological Basis for the Theory of Music, 2nd English Edition (A. Ellis). This passage was written 135 years ago. Yet we still have no unique accepted formal foundation for going beyond what Helmholtz brilliantly saw as the building blocks he called "musical tones", which we now call "frequency". Helmholtz also saw that "beats of simple tones" and "beats due to combinational tones" or "differential tones" [op. cit., Page 159] formed sum and difference beats. Generations of engineers went on to generalize and heavily capitalize this notion of "modulation". The hand-held revolution has been heavily dependent on it. Over the last 15 years our University of Washington Lab has refined a sum-of-products model of natural signals, such as speech and music, where low frequency information-bearing waveforms modulate higher frequency carriers. While this basic view is not new, careful analysis shows that, in general, past assumptions that carriers are narrowband, and that modulators are non-negative and real, is incorrect. Deeper analysis shows that these past assumptions break down and more information is available when there is: 1) significant statistical correlation between real and imaginary parts of the modulators and 2) significant correlation between differing frequency regions of the original signal. The above theoretical results have had practical impact. For example, our recent results show how improved analysis of sonar and enhancement of reverberant speech signals (like the echoes heard in speakerphones) is possible. Also, as was just publicized on National Public Radio (goo.gl/KkultV), we will show how it is now possible, in the few patients we have tested, to encode musical timbre (the difference between musical instruments) for cochlear implants for the profoundly deaf. More work remains from these new views and the impact could extend beyond one-dimensional acoustic signals. This research is joint with many others and is currently supported by the Wallace H. Coulter Foundation, the Army Research Office, and the Office of Naval Research.