Why Is There Always a Hiss? Nothing Is Ever Completely Silent

Random fluctuation arises from physics rather than from poor engineering, so it cannot be designed away entirely. Thermal motion of electrons in any conductor above absolute zero generates a randomly varying voltage across it, and the level depends only on the temperature, the resistance and the range of frequencies being measured. Current flowing as discrete charges produces a further fluctuation, since the arrivals are random. Components add their own. Together those set a floor below which a real signal cannot be distinguished from the fluctuation, and the whole design of a sensitive instrument is an effort to get the signal well above it.

Several approaches lower the floor or lift the signal above it:

• •Cooling the sensor, since thermal fluctuation falls with temperature
• •Narrowing the range of frequencies accepted, since noise scales with it
• •Averaging many measurements, since random fluctuation partly cancels
• •Modulating the signal so it can be separated from the background
• •Choosing low-noise components at the first stage, which dominates
• •Increasing the signal itself, which is frequently the cheapest option

Repeating a measurement and averaging improves the result because random fluctuation adds up differently from a consistent signal. The signal accumulates in proportion to the number of measurements while random fluctuation accumulates in proportion to the square root of that number, so the ratio between them improves with the square root of the measurements taken. That is genuinely useful and has diminishing returns built in, since improving by a factor of ten requires a hundred times as many measurements. It also fails entirely against anything that is not random, so a steady interference or a drift in the instrument is not removed by averaging at all and must be dealt with some other way.

Comparing instruments requires stating the level in a defined way, and the conventions catch people out. A figure is meaningless without the bandwidth it was measured over, since accepting a wider range of frequencies admits proportionally more noise, so specifications state a level per unit of bandwidth rather than an absolute. Audio equipment quotes a ratio between the largest signal it handles and the background, which describes the usable range rather than the floor itself. Radio receivers quote a figure comparing their own contribution against the unavoidable thermal minimum. In each case the number describes a relationship, and quoting one without its reference tells the reader almost nothing.

Adding fluctuation on purpose sounds perverse and is standard practice in several fields. Digital audio and imaging add a small amount before converting to digital, which breaks up the regular error pattern that quantisation would otherwise produce, converting an audible or visible artefact into a much less objectionable hiss or grain. Encryption and secure systems use genuinely random sources deliberately. Some sensing techniques exploit the effect in which a small amount of fluctuation actually helps a weak signal cross a detection threshold. And masking noise is played in offices and in hospitals to make speech from elsewhere less intelligible.

Thermal motion of electrons and the discrete arrival of charges produce random fluctuation in any system above absolute zero, which sets the smallest signal that can be distinguished. Cooling, narrowing the frequency range and averaging all help, with averaging improving only as the square root of the number of measurements and doing nothing against interference that is not random.