Illustrated Physics
physics, drawn
Concept

Signal to noise ratio — where it appears

The ratio of a signal's power to the power of the noise accompanying it, usually quoted in decibels. It sets the faintest signal a receiver can detect and the precision of any measurement made from it, and filters, averaging and coherent integration exist to raise it.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Too little noise, the right amount, too much. The particle's position over 8 cycles of the push (thin grey line, scaled to the wells), with noise of intensity 0.03, 0.085, 0.3 (top to bottom), the barrier being 0.25. With little noise it stays almost always in its starting well and only trembles: 0 hops in eight cycles. With noise 0.085 it hops 30 times, almost always once per half-cycle and almost always while the push is helping — a clean square wave following a push too weak to cause a single hop. With noise 0.3 it hops 285 times, at random, and the push is lost again. There is a best amount of noise, and it is not zero.

The noise that helps a weak signal through

A system that can sit in either of two states, nudged back and forth by a periodic push too weak to switch it, does nothing at all — until noise is added. Then it begins to switch, and with the right amount of noise it switches in step with the push, once each half-cycle, as though the push had been strong enough all along. Too little noise and it never switches; too much and it switches at random. The response peaks at a nonzero noise, which is why the effect is called a resonance, and why crayfish, paddlefish and human fingertips appear to use it.

waves · Resonance The long pulse that arrives as a spike. The output of the matched filter for the chirp, in decibels against delay in units of 1/B, beside the same filter's output for an unmodulated pulse of the same duration (dashed). The plain pulse's echo is a broad triangle 100 units wide; the chirp's is a spike 0.878/B wide at its half-power points — compressed by the time-bandwidth product, 50. The compression is not free of shape: the spike has sidelobes, the first at −13.6 dB, from the abrupt edges of the band, and a weak echo sitting in a strong echo's sidelobe can be hidden by it. The energy is all there — the filter has concentrated the whole pulse's echo into one instant of output.

The long pulse that arrives as a spike

A radar that wants to see far must send a lot of energy, and a transmitter limited in peak power can only do that with a long pulse; a radar that wants to tell close targets apart needs a short one. A chirp — a pulse whose pitch rises steadily from start to finish — is both. Received through a filter that delays its low notes more than its high ones, every part of the echo arrives at the same instant, and fifty microseconds of pulse leave the receiver as a spike one microsecond wide. Resolution turns out to belong to bandwidth, not to duration, and the price of the trick is paid in sidelobes and in a target's speed being mistaken for its range.

waves · Wave packets

Named alongside it

The objects these essays reach for when they reach for this one.

BandwidthBistabilityChirped pulse amplificationCorrelationKramers rateNoiseRadarResolutionSidelobesStochastic resonanceSynchronisationThreshold

All concepts