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Random thoughts on noise

Generally we think of noise as an unwanted, irrelevant artifact.  Almost always in acoustics, electrical engineering, and applied physics, the goal is to reduce noise, or at least to extract useful information from a noisy signal.  In our daily lives, it seems that acoustic noise is a constant, if not conscious presence.

Human brains are amazingly adept at filtering noise from both auditory and visual sources.  No current computational algorithm can even come close to matching the brain’s performance on distinguishing noise from relevant information.

In applied mathematics, the term white noise has a very precise definition.  In fact many equivalent definitions–perhaps the simplest being the derivative of the Wiener process (also known as Brownian motion).  One of its characteristics is a constant spectral power density.  This noise turns out to be an extremely important concept which appears in many different contexts, including finance, diffusion processes, quantum mechanics, electronics, and communications.  In all of these areas, an analytical understanding of noise and its properties leads to great insights into the behavior of real systems.

Audible filtered white noise can actually be quite pleasant.  Think of the sound of a soft rain, the rustling of dry leaves in the fall, wind in the trees, or waves on the beach–each sound has a lot in common with filtered white noise.

It may be that one way of distinguishing between annoying noise and pleasant noise is asking whether there is a possibility that some portion of the sound may contain something important.  Processing noise that may contain interesting information, like the randomly overlapping voices at a party, requires much more mental energy than simply enjoying the natural sound of a waterfall.  It is very hard to ignore voices, even when they are not speaking to us.  Presumably this is more distracting.

Taking this idea a little further, information theory relates information to changes in entropy.  Audible white noise (and pink noise, and brown noise) has greater entropy, and contains less information, than speech, rock concerts, and the sound of your neighbor’s lawnmower.   It would be interesting to study whether or not there is a substantial correlation between information content, and the perceived level of annoyance of sounds.  (If any readers are aware of such studies, we would love to hear about them.)

In certain very specific situations, noise can actually make signals easier to detect and interpret.  This is called stochastic resonance.  It happens when there is a nonlinear detection process (such as a simple threshold), and the addition of noise to a weak signal brings the sum, on average, into a more easily detectable range.

Clearly noise has different meanings in different contexts.  Furthermore, there are large variations among individuals as to what constitutes noise.  Of course, even the same person might define noise differently depending on the time of day or the circumstances under which a particular sound is heard.

No real conclusion here.  Okay, maybe just one: the single word “noise” is inadequate to convey all of the meanings and connotations we ascribe to it.

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1 Comment

  • Interesting thoughts, but your assessment of information content is not quite right. A simple, perfectly repeating sound (e.g., a continuous jack hammer or or pile driver) has entropy of 0. It’s the irregularities that increase the information content in a Shannon sense. White noise, if truly a random sequence of amplitudes (delta function correlation, flat spectrum), has high entropy. — So the logic that information content relates to annoyance or ability to distract is not consistent over the entire range of values. However, I think it does provide a basis for understanding why introducing small variations in, e.g., the period of pile driver, does seem to increase the annoyance it causes.

    js


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