A 1 GiB memory pulse, observed two ways: as the continuous signal it physically is, and through a sampler whose interval and integration window can vary. The same workload renders correctly under one set of sampler parameters and misleadingly under others.
The generator signal
A 1 GiB anonymous allocation held for 3 s, released, re-allocated 44 s later. Strictly periodic; instantaneous rise and fall; duty cycle 3/44 ≈ 6.8 %. The top panel renders this exactly.
Reconstruction mathematics
The pulse train decomposes into a Fourier series with components at f₀, 2f₀, 3f₀, …, where f₀ = 1/44 Hz. The sampler’s Nyquist frequency is fₛ / 2 = 1 / (2 · interval); any harmonic above it folds into the baseband at |f mod fₛ|. The integration window contributes a sinc-shaped low-pass envelope: at window = 0 every harmonic folds without attenuation, and as the window grows, higher-frequency content is suppressed before it can alias. LCM(interval, 44 s) sets the recurrence period of the visible pattern.
Pathologies
Bimodal LCM clustering — point sample, interval 30 s. Over each 660-second LCM cycle the sampler catches the pulse exactly twice, 90 s apart, then runs silent for 9.5 minutes. The dashboard reads as a rare outlier rather than a 6.8 % duty-cycle steady state.
Amplitude smearing — integrating window between zero and the pulse period (try interval 30 s, window 10 s). Each scrape returns the mean over a partial pulse: values land between ~100 MiB and ~300 MiB but never reach 1 GiB. Hits look frequent; the dashboard reads as noise when the underlying signal is strictly binary.
DC convergence — integrating window much greater than the pulse period (try interval 30 s, window 60 s). The signal converges to its duty-cycle-weighted mean, ≈ 70 MiB. The pulse structure is gone entirely; the dashboard reads as a quiet steady-state load.