Free Physics & signals lessons
Stable distinctions in a noisy world
A physical device exposes a continuous quantity such as voltage, charge, light, or magnetization. Engineers assign ranges of that quantity to symbols. A receiver uses thresholds to decide which symbol arrived; the unused gap between valid ranges provides a noise margin.
Suppose 0–0.8 V means low and 2–3.3 V means high. A gate receiving 2.7 V does not forward “2.7” as an increasingly degraded fact; it produces a fresh high-level output. Cascaded gates therefore restore logical levels, within their timing and electrical limits.
What measurement keeps—and loses
Sampling chooses when to observe a changing signal; quantization chooses the nearest representable amplitude. Sampling too slowly can make a high-frequency pattern masquerade as a slower one—aliasing. Too few amplitude levels introduce quantization error. More samples and bits improve fidelity but consume bandwidth, storage, and energy.
Frequencies above the representable range can fold into false lower frequencies after sampling. Once folded, the samples no longer reveal which frequency was original. A low-pass filter removes those components before the irreversible sampling step.
Bandwidth, latency, energy, and synchronization
Bandwidth limits how much variation a channel can carry; latency measures how long a change takes to matter at the destination. Receivers also need timing—an explicit or recoverable clock—to decide where one symbol ends and the next begins. Faster signalling usually tightens noise, power, and synchronization constraints.
Overlaying many received symbol intervals reveals an “eye.” Vertical closure indicates reduced voltage margin; horizontal closure indicates timing uncertainty. Sampling near the widest opening maximizes tolerance. The diagram joins analog behaviour to the probability of digital mistakes.
Detect corruption and locate the broken boundary
The sender encodes symbols with known structure. The channel perturbs them. The receiver measures, decides, and checks whether the result satisfies that structure. A parity bit can detect some errors; stronger codes add enough redundancy to locate or correct patterns of corruption.
If raw sensor readings are already clipped, no packet code can restore the lost amplitudes. If local readings are sound but checksums fail, investigate the channel. If frames pass checks yet values are wrong, inspect decoding, units, and schema. Each observation narrows the failed boundary.