sampling

Direction tested: sampling INSTANCE_OF method. Law 9: sampling is a specific kind of method — a methodological technique. A competent speaker would call sampling 'a method.' Files against the nearest general kind.

Direction tested: random-sampling INSTANCE_OF sampling. Random sampling IS a specific kind of sampling — selecting a subset using a chance mechanism with known probabilities. A competent speaker would call it a type of sampling. Law 9 test passes.

Stratification is a specific kind of sampling technique — the population is divided into strata and sampled from each. Specific→general per Law 9: a competent speaker would call stratification 'a sampling method'. Nearest kind is sampling; no intervening rung on the ladder.

Standard error measures the variability of a sample statistic across repeated samples. Remove sampling as a concept, and standard error has nothing to operate on — it is literally the standard deviation of the sampling distribution. This is a constitutive, present-tense dependency.

Which-came-first test: sampling (as the act of discretizing a continuous signal) predates aliasing as a named concept, but the direction here is DEPENDS_ON not DERIVED_FROM. Removal test: remove sampling and aliasing stops operating entirely — aliasing only occurs when a continuous signal is discretely sampled. Without sampling there is no aliasing. The dependency is constitutive.

Anti-aliasing-filter is a signal-processing circuit or algorithm designed for the sake of sampling — it attenuates out-of-band frequencies to ensure sampling produces faithful discrete representations. Its entire design purpose is to serve sampling quality.

The Nyquist criterion is a mathematical rule specifically about sampling rates — fs > 2·f_max. Remove the concept of sampling and the criterion ceases to operate in any domain. Law 8 removal test passes.

The anti-aliasing filter concept derives from sampling theory: without sampling, there is no aliasing problem. The Nyquist-Shannon sampling theorem (1928) established the aliasing phenomenon, and anti-aliasing filters were developed as the practical solution. Which existed first? Sampling (as a mathematical concept) predates the anti-aliasing filter (as a named engineering construct). DERIVED_FROM: sampling → anti-aliasing-filter.

Frequency resolution as a signal-processing parameter derives from sampling theory: the resolution limit Δf = 1/(N·Ts) is determined by sampling rate and count. Sampling theory (Nyquist-Shannon, 1928) predates and established the framework within which frequency resolution is defined. Historical chain is correct per Law 7.

The concept of aliasing as a named signal processing phenomenon emerged from the practice of sampling — it was identified when engineers noticed that undersampling caused different frequency components to become indistinguishable. Sampling (the practice) predates aliasing (the concept). The which-came-first test: sampling existed first and fed into the concept of aliasing.

The Nyquist frequency (half the sampling rate) is a concept derived from sampling theory. Nyquist (1928) formalized the maximum representable frequency within the framework of sampling. Which-came-first: sampling as a concept predates the specific frequency-limit concept.

Sample-and-hold is a specific technique for capturing and holding the instantaneous value of a continuous-time signal. It is a particular kind of sampling operation — a method of sampling that includes both the capture (sample) and the retention (hold) phases. Nearest kind: sampling.

anti-aliasing is built and maintained for the sake of sampling — it prevents aliasing artifacts that corrupt sampled data. Its design purpose is to ensure sampling operates correctly. The test: remove anti-aliasing and sampling produces corrupted (aliased) results. Servant (anti-aliasing) points at master (sampling).

Oversampling is a specialized form of sampling that operates at rates far above Nyquist. Remove sampling from the picture and oversampling cannot operate — it needs the sampling framework as its foundation. The which-came-first test confirms sampling (0.14) predates oversampling (0.99).

A sample-rate-converter operates on sampled audio; without sampling there is no signal to convert. Remove sampling and the converter has nothing to process.

Oversampling is a specific kind of sampling — sampling above the Nyquist rate. Law 9: specific→general. The which-came-first test (epoch: oversampling 0.17, sampling 0.14) confirms sampling is older/more-foundational, consistent with the kind-of hierarchy.

Oversampling as a technique was formulated after sampling theory was established; it extends sampling by taking more samples than Nyquist requires. Which-came-first test per Law 7: sampling predates oversampling.

Audio-jitter measures timing variation in sample delivery/playback. Remove sampling (the discrete sample framework) and jitter as a measurable deviation from expected sample timing ceases to exist. Law 8b.

audio-clock-drift is the phenomenon where a sampling clock varies from its nominal rate — it fundamentally depends on the sampling process to exist as a concept. Remove sampling and there is no clock to drift, no sampling instants to misalign. The drift is a property of the sampling mechanism's timing.

pitch-shifting algorithms (like PSOLA or phase-vocoder) depend on sampling — they operate on discrete audio samples and the pitch-shifting mechanism works by manipulating sample-level timing and phase. Remove sampling and the algorithm has no data structure to operate on.

Anti-aliasing is a technique that only exists in the context of sampling — its purpose is to prevent aliasing artifacts that arise from the Nyquist sampling theorem. Remove sampling as the reference operation and anti-aliasing has no definition or mechanism.

Decimation reduces sample rate by an integer factor — its operation is defined by the sampling framework. Remove sampling and decimation has no mechanism or definition.