Concept

Aliasing — where it appears

What happens when a sampler and the pattern it samples share a period, so the pattern vanishes from the measurement. A window that retires a block every fixed number of arrivals is such a sampler, and against a repeating burst it reports a perfectly even stream while the arrivals are grossly bunched.

Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.

even5.1 s – 5.1 s1.00× · dispersion 0.00Poisson4.7 s – 5.5 s1.16× · dispersion 0.70bursty4.5 s – 4.5 s1.00× · dispersion 0.57drifting565 ms – 14.8 s26.14× · dispersion 849.57duration one block covered4,096 arrivals in 8 blocks · 100 Hz · 1 ms clock26.1× on the drifting stream

The window that is even in the wrong currency

A window of four thousand arrivals in eight blocks retires a block every 5.1 seconds on a steady stream and anywhere between 0.57 and 14.8 seconds on a stream whose rate moves. The structure cannot tell, because it is counting arrivals, and the alert written against it is in seconds.

streaming · Window
1.821251.951.431752.731.302253.521.292503.911.183755.861.005128.00longest block ÷ shortestarrivals per block, and bursts per blockpart of a bursta whole numberbursts of 64 · 8 blocks · 20,000 arrivalsdispersion 0.57 and a ratio of 1.00

The boundary that hides the burst

A window whose blocks hold five hundred and twelve arrivals reports a perfectly even stream — every block the same duration to the tick — while the arrivals it is retiring have an index of dispersion of 0.57. Move the block to a hundred and twenty-five and the same stream varies by 1.8 times.

wrong · Window
1 — no differencethe whole array reviewed1.03×only this batch reviewed1.22×a block window, which does alias1.48×20,000 arrivals · period 50 · cyclethe instrument reads 1.48 where an alias is known to be

The sampler that cannot alias

A block window's boundary fires on an arrival count, and a stream whose burst repeats every sixty-four arrivals is reported as perfectly even by a block of five hundred and twelve. A quantile summary compresses on an update count, which is the same arrangement. Swept against three periodic value processes and their shuffles, it does not alias — and the reason is one line of arithmetic rather than a lucky sweep.

wrong · Window

Named alongside it

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

Arrival processBurstinessMeasurementSliding windowTemporal resolutionClock resolutionCommensurabilityExpiryExponential histogramFailure modeOccupancySampling

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