Noise in the time dimension: the strange case of flicker

-January 17, 2013

The concept of noise brings to mind static, a bad cell-phone connection, a poorly tuned radio or television, pixel-freakout on TV.

Clocks have noise, too. The time between ticks on your watch is not exactly one second. The time between this tick and [wait a second] this tick is not exactly the same. Other than things that you count, like the number of people in a room, every measurement suffers uncertainty and imprecision.

Figure 1: Flicker is everywhere.

Timing noise in digital electronics is called jitter and it’s a big problem for design engineers. It causes errors—pixel freakout on TV, audio crackup on cell phones, and errors on networks can even screw up your bank balance. Optimizing cost and performance means using the cheapest clocks capable of driving processors and transmitters at an acceptable error rate.

Of the many sources of timing imprecision, one is shrouded in mystery and intrigue because it shows up in so many places and lacks a satisfying cause: flicker.

Flicker shows up in every type of oscillator including:
•    the human heart, brain waves, music (pleasing melodies, in particular), paintings, cartoons
•    stock market, GDP, human reaction times, stars, quasars
•    avalanches, earthquakes, and meteorology
•    Every electrical system, both digital and analog, most notably at the physical layer in oscillators and resistors (which covers everything) and a bit higher than physical in digital signal processing (DSP).

The ubiquitous nature of flicker indicates something deep and fundamental. It reminds me of a novel by James Joyce; there’s something incredibly deep and moving in Ulysses but I have no idea what it is.

Flicker lies between purely random white noise, think of your TV with no signal, and random walk (Brownian or red) noise. White noise isn’t correlated to the signal, it’s just equal levels of noise at every frequency with no temporal correlation between increments. Random walk noise, on the other hand is random but with a bias. A random walk is easier to relate to as a drunken walk with a destination. Going from the bar to the house, each step is random but with a tendency toward the house. That is, eventually the drunk makes it home, but with lots of noisy steps along the way.

Flicker’s mystery and intrigue comes from its mathematical description. A description that is shockingly similar to how one describes distantly related events but with no motivation. That is, flicker noise on stars seems to indicate a correlation of events separated by large distances and times. In financial markets, it’s like a stock’s current price is affected by the price from a long time ago. Similarly, in electric circuits, it appears as though the behavior of electrons at one end of the conductor affects electrons at the other; as though they queue up for excitation and absorption under a voltage. But unlike random walk noise, flicker has no clear link to the forces that drive the system.

The mystery puts us in the correlation-is-not causation purgatory. There must be something in common, a general explanation for the correlation if not the cause. In other words, there’s something incredibly deep and moving in flicker but I have no idea what it is.

It’s just like Ulysses only different.

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