When I discuss analog computation with most people, their instant reaction is to explain to me that there is no such thing as analog. For instance, one of the comments on an earlier post I wrote on analog vision pointed out that using a film-based camera rather than a digital camera doesn't give you infinite resolution, just a higher, finite resolution. In this case the the limit is grains of silver on the film rather than the number of pixels on a camera array. This is true, but it also misses the point.

One of the main differences between physical computation (the slightly extreme form of analog I discussed in my PhD thesis) and digital computation is that it is good at extracting meaning out of tiny fluctuations. Digital computing, for very good reasons, is designed so that small 'glitches' that could lead a calculation astray are completely ignored. This is great when doing maths, but not when processing signals.

Let me give a concrete example from a piece of research done a few years ago by Dana Anderson and his colleagues at the University of Colorado: a classic example, in my view, of how analog feedback can be exploited to pull signal from noise. Essentially the system (shown) performs a winner-take-all operation to solve the so-called 'cocktail party' problem where lots of noise (literally sounds in this case) overlaps making it impossible to hear what is going on. In his system, one of the components (one of the sounds) will dominate, extinguishing the rest.

Note: this system is really complicated optically, so don't feel bad if you don't understand my explanation on the first pass.

First, the sound signals are processed (you can see the details one of their publications on the subject or on their website) and then used to vary the output of an array of laser beams (so the light carries the sound). These beams create a holographic pattern in the photorefractive medium, a crystal that changes the way it bends light when it is exposed to photons of a particular color. This pattern is then read out by another beam (called the 'loop' beam because of the shape of the circuit) that, as well as picking up information, helps strengthen the hologram where the patterns are similar, and weaken it where the patterns are not.

The loop beam is then made to interfere with a second beam with a similar but not identical frequency. This produces beats (where two high-frequency signals, mixed, produce a frequency that is the difference between the two). This new oscillation is low enough to be picked up by a detector. After being filtered and amplified, this signal is used to modulate the phase of the loop beam, altering the elements of the hologram that are strengthened and weakened by it.

In English, the loop beam initially reads out a hologram containing all of the signals. Since one is the strongest (even if only by a tiny amount) it has slightly more impact on the beam, and so also on the output of the detector. The feedback loop is then tweaked to enhance this effect. This feedback continues until the strongest signal becomes the only signal (winner takes all). You can actually hear this happening in their system if you use the player below the diagram.

We know we have winner-take-all circuits in the eye, so this kind of feedback is not just clever engineering, but biologically sound too. Even the tiniest hint of what's important can be leveraged into fuller knowledge. Of course, you can do feedback with digital too, but that would be silly: essentially you would be asking it to do something it was designed not to be good at. And, as I will discuss in a future post, you will pay a huge power penalty for your trouble.

Figure: This holographic systems pulls out individual sounds from noise using feedback. Click the image to hear this happen.