The accepted ontology
Browse accepted Systema Constructum entries: human-made tools, institutions, methods, practices, works, and their definitions.
100 entries in this page
Sidechain is a human-made audio routing technique where the control signal for a dynamics processor is derived from a different audio source than the signal being processed. Parameters: (1) source input — the audio signal that triggers detection; (2) target i…
Ducking is a human-made audio dynamics technique that automatically reduces the gain of one signal when another signal is present, typically using a sidechain detector to trigger attenuation of the background signal in response to a foreground signal. Paramet…
A clipper is a human-made audio dynamics processor that limits signal peaks by truncating the waveform at a set threshold, producing characteristic flat-topped distortion and harmonic content. Parameters: (1) clip threshold — the amplitude level at which clip…
A saturator is a human-made audio effects processor that drives a modeled or real nonlinear circuit (tube, transformer, tape, or transistor) into mild saturation, adding even-order and odd-order harmonics to enrich the signal's timbre without full clipping. P…
A de-esser is a human-made audio dynamics processor that attenuates sibilant high-frequency energy, typically 4–10 kHz, in vocal or instrumental signals to reduce excessive 's' and 'sh' sounds. Parameters: (1) detection frequency range — the band where sibila…
A limiter is a human-made audio dynamics processor that automatically reduces gain when an input signal exceeds a set threshold, clamping the output to a maximum level to prevent overload or distortion. Parameters: (1) threshold — the signal level at which li…
A preamp is a human-made electronic circuit whose purpose is to increase the amplitude of a weak input signal to a line-level or suitable operating level for subsequent processing stages. Parameters: (1) input gain — the amplification factor applied to the in…
Overlap-save is a human-made signal processing technique for efficient linear convolution that computes the output by processing overlapping blocks of input and discarding the overlapped portions, using FFT-based multiplication and a save operation to reconst…
A tape-loop is a closed magnetic tape path with record and playback heads spaced along the loop, driven by a capstan motor at constant speed, so the signal recorded at one head is replayed after a fixed mechanical delay determined by head spacing and tape spe…
A comparator is a human-made electronic circuit or system that compares two input signals and produces an output indicating their relationship — typically whether one exceeds the other, whether they are equal, or which is larger. Parameters: (1) reference inp…
Bit-crusher is a human-made audio effect that reduces the bit depth and sample rate of a digital audio signal to produce quantization noise, aliasing, and lo-fi timbral distortion. Parameters: (1) bit depth reduction — target resolution from 24/16 down to 1-8…
Headroom is the margin between a system's nominal operating level and its maximum capacity before distortion or clipping occurs. The parameters are nominal level, maximum level, and the type of limiting applied; the mechanism of persistence is engineering spe…
Clipping is the waveform distortion that occurs when a signal's amplitude exceeds the maximum processing capacity of a system, causing the signal's peaks or troughs to be truncated at the system's amplitude ceiling. It manifests as hard clipping (abrupt trunc…
Gain is the measure of amplification factor — the ratio of an output signal magnitude to its corresponding input signal magnitude. It quantifies how much a system (amplifier, attenuator, filter stage) multiplies a signal's amplitude, expressed either as a dim…
An amplifier is an electronic circuit or device that increases the amplitude of an input electrical signal to produce a larger output signal, while attempting to preserve the original waveform's shape and information content. It operates by using external pow…
Tape delay is a human-made echo effect that records an audio signal onto a continuous magnetic tape loop driven by capstans, then reads it back from a playback head positioned a fixed distance downstream so the signal returns after a time set by tape speed an…
A phase-locked loop is a human-made feedback control system that locks the phase and frequency of an internally generated signal to those of a reference input signal. It comprises three functional stages: (1) a phase detector (or phase/frequency discriminator…
Waveshaping is a human-made nonlinear signal-processing method that generates harmonics by applying a static amplitude transfer function to an audio signal, mapping input amplitude to output amplitude through a deliberately nonlinear curve. Parameters: (1) tr…
sample-clock is a human-made timing reference used to govern the discrete sampling of a continuous signal in digital audio, data acquisition, and synchronous systems. It provides a periodic electrical signal that determines the instants at which an analog-to-…
A harmonic exciter is a human-made audio processing device or algorithm that adds upper harmonics to a source signal to increase perceived presence, clarity, and brightness. Parameters: drive/excitation amount (how much harmonic content is added), mix/blend r…
A pitch-shifter is a human-made audio processing technique and device that changes the pitch of an audio signal (its fundamental frequency and harmonic structure) while preserving its duration, in contrast to playback-speed changes that trade pitch for time.…
Tape saturation is an audio effect technique that simulates the non-linear harmonic distortion, soft clipping, and level-dependent compression produced when an analog magnetic tape recorder is driven beyond its linear operating range. Parameters: (1) input dr…
Delay is a human-made audio effect technique that takes an input signal, stores it in a delay line, and returns discrete repeats of that signal at fixed or modulated time intervals, mixing the repeats back with the dry signal. Parameters: (1) delay time — the…
A wah-pedal is a guitar effects device that sweeps the center frequency of a bandpass filter using a foot-operated control (typically a potentiometer linked to a spring-loaded rocker), producing a vowel-like timbral sweep. Parameters: filter bandwidth (Q), sw…
Overdrive is a signal-processing effect created by driving an amplifier or preamplifier circuit beyond its linear operating range, producing soft clipping that adds warm even-order harmonics to the audio signal. Parameters: input drive level, gain staging, ou…
A sampler records audio segments into digital memory and replays them at different pitches and tempos, triggered by performance input such as a keyboard or MIDI signal. Its parameters include sample length (how much audio is captured), play mode (one-shot, lo…
A synthesizer generates sound electronically using oscillators to create waveforms, filters to shape timbre, and envelope generators to control how parameters evolve over time. Its parameters include oscillator type (sine, sawtooth, square, etc.), filter cuto…
Noise-gate is an audio processing device or algorithm that automatically attenuates or mutes an audio signal when its amplitude falls below a user-set threshold level, thereby reducing background noise between intentional sound events. Parameters include thre…
Equalizer is an audio processing device or algorithm that splits an audio signal into multiple frequency bands and independently adjusts the gain (amplification or attenuation) of each band, enabling precise tonal shaping and spectral balancing of a sound sou…
Distortion is an audio effect produced by driving an electronic signal beyond the linear operating range of a circuit or algorithm, causing clipping (hard or soft) that generates new harmonic and subharmonic frequencies, thereby adding grit, warmth, or aggres…
A phaser is a human-made audio effect technique that mixes a dry signal with a phase-shifted version of itself, producing a sweeping comb-filter 'swoosh' sound. Mechanism: the input signal is split into two paths — one remains dry, the other passes through a…
A wah-wah is a human-made audio effect technique that sweeps the center frequency of a bandpass filter over time, producing a vocal-like 'wah' sound. Mechanism: the input signal passes through a bandpass filter whose center frequency is modulated by a low-fre…
Vibrato is an audio effect that produces a slow, periodic variation in the pitch (frequency) of a sound signal, creating a wavering or throbbing quality. The mechanism uses a low-frequency oscillator — classically a sine wave at 4-8 Hz — to modulate the frequ…
Tremolo is an audio effect that produces periodic variation in the amplitude (volume) of a sound signal, creating a pulsating or quavering effect. The mechanism uses a low-frequency oscillator (LFO) to modulate the amplitude envelope of the audio signal: the…
An audio effect is a signal processing technique or device that intentionally alters a sound signal to change its perceptual character, creating a version that is distinguishable from the unprocessed source. Effects are categorized by their sonic result (dist…
Chorus is an audio processing technique that takes an input signal, creates one or more duplicates, applies a low-frequency oscillator to vary the pitch (typically ±5–20 cents) and delay time (typically 15–40 ms) of each copy, and mixes the processed copies b…
Frequency modulation is a technique of signal processing in which the instantaneous frequency of a higher-frequency carrier signal is varied in proportion to the amplitude of a lower-frequency modulating signal: the carrier's phase continuously accumulates th…
A compressor reduces the dynamic range of an audio signal by attenuating levels above a set threshold. Parameters: threshold (dB level above which compression activates), ratio (attenuation amount above threshold, e.g. 4:1), attack time (response time to reac…
Amplitude modulation is a signal processing technique where the amplitude of a higher-frequency carrier signal is varied proportionally by a lower-frequency modulating signal. The output contains the original carrier frequency plus upper and lower sidebands a…
A ring modulator is a signal processing effect that multiplies two input signals (carrier and modulator) together, producing output frequencies at the sum and difference of the input frequencies (f1+f2 and |f1-f2|). The original input frequencies are suppress…
A reverb is a sound processing technique that creates the acoustic effect of reflections in an enclosed space. Parameters include decay time (duration of the reflection tail), pre-delay (time before reflections begin), diffusion (density of reflections), and…
An oscillator is a human-made signal source that, while powered, sustains a periodic output without any periodic input — a steady energy supply converted into rhythm. Its parameters are: (1) frequency — the designed repetition rate, from sub-Hertz to gigahert…
A delay-line is a signal storage and retrieval construct that records an input signal and releases a copy after a controlled time offset (delay time). Its parameters are: delay time (duration of lag, from microseconds to seconds), input/output bandwidth, and…
An LFO (low-frequency oscillator) is a signal generator that produces periodic waveforms — typically sine, square, triangle, or sawtooth — at frequencies below the human audible range (conventionally 0.01 Hz to 20 Hz). Unlike audio-rate oscillators, LFOs are…
A comb-filter is a signal processing technique that produces a frequency response characterized by a series of equally spaced spectral peaks and nulls (resembling a comb). It operates by adding a delayed and scaled copy of an input signal to the original sign…
A flanger is a human-made audio effect technique that produces a sweeping comb-filter 'jet' sound by summing a signal with a short delayed copy of itself whose delay length is slowly modulated by a low-frequency oscillator. Mechanism: the dry signal is mixed…
Spectral flanger is a human-made audio effect technique that produces the flanger's characteristic moving comb-filter notches by realizing the flanging delay in the frequency domain instead of as a time-domain delay line. Mechanism: the input is decomposed in…
A pitch-shift procedure transforms the fundamental frequency of an audio signal using spectral methods — typically the phase-vocoder or overlapping-window approach — by modifying phase relationships across short-time Fourier transform frames and resynthesizin…
A tool whose prime mover in operation is the human hand: an implement whose graspable form and working end are shaped so that the hand alone — by grip, strike, twist, or motion — applies the force, motion, or precision the task requires. Its parameters are: (…
A discrete-signal reconstruction method that places new samples at non-integer positions: each target sample is a weighted sum of its neighboring samples, the weights being the sinc kernel sin(pi*x)/(pi*x) evaluated at their distances, and that infinite non-c…
Contrastive divergence is a human-made approximate learning algorithm for energy-based models, especially Boltzmann machines, that estimates the gradient of the log-likelihood by running a short Gibbs chain initialized from data and contrasting the data stati…
A real-valued function on R^n defined as log-sum-exp(x) = log(∑_{i=1}^n exp(x_i)), where log is the natural logarithm. It is a smooth, differentiable approximation to max(x), with the bound max(x) ≤ log-sum-exp(x) ≤ max(x) + log(n). The function persists thro…
A family of probability distributions on a common support, parameterized by a natural parameter vector η∈Θ⊆R^k, whose density (w.r.t. a base measure μ) takes the canonical form p(x|η) = h(x) exp(η·T(x) − A(η)), where T(x) is the sufficient-statistic vector, A…
Natural gradient is a human-made optimization algorithm that modifies standard gradient descent by multiplying the gradient by the inverse Fisher information matrix, effectively following the steepest descent in the Riemannian manifold of probability distribu…
Information geometry is a human-made mathematical framework that equips families of probability distributions with the structure of a differentiable manifold, where the Fisher information matrix serves as the Riemannian metric tensor on the parameter space. P…
Cepstral peak prominence is a human-made metric that quantifies the strength of periodicity in a time-domain signal by analyzing the magnitude of the peak in the real cepstrum, typically computed from the log magnitude spectrum of a windowed frame. Parameters…
Power divergence is a family of statistical divergences between two probability distributions P and Q, parameterized by a real number α ≠ 0,1. The general form is D_α(P||Q) = (1/(α(α-1))) Σ (p^α q^(1-α) - ...) with specific special cases: α=1 gives Pearson ch…
Bias-variance decomposition expresses the expected squared error of an estimator f̂ for target f(x) under loss (y−f̂(x))² as E[(y−f̂)²] = Bias²(f̂) + Var(f̂) + σ², where Bias² = (E[f̂]−f)², Var = E[(f̂−E[f̂])²], and σ² is irreducible noise variance. Parameter…
Variance is the second central moment of a random variable or probability distribution: Var(X) = E[(X - E[X])^2] = E[X^2] - (E[X])^2. Its parameters are a probability space and a real-valued random variable X with finite second moment; for a discrete distribu…
Rényi entropy of order α for a discrete probability distribution P = {p_i} is H_α(P) = (1/(1-α)) · log(Σ_i p_i^α), for α ≥ 0, α ≠ 1. At α = 1 it reduces to Shannon entropy by continuous limit. For α → 0 it gives Hartley entropy; for α → ∞ it gives min-entropy…
A Tsallis divergence is a human-made family of statistical divergences between probability distributions P and Q, parameterized by the order q (q ≠ 0, q ≠ 1). It is defined as D_q(P||Q) = (1/(q - 1)) · (1 - Σ_i p_i^q / q_i^(q - 1)) in the discrete case, where…
The likelihood function is a human-made function L(θ | x) = p(x | θ) that maps each parameter value θ in a statistical model's parameter space to the probability (or probability density) of observing the fixed data x under that parameter. Its parameters are t…
The Rényi divergence of order α (α ≥ 0, α ≠ 1) is a human-made family of statistical divergences between probability distributions P and Q, parameterized by the order α. It is defined as D_α(P‖Q) = (1/(α−1)) · log(Σ_x P(x)^α · Q(x)^(1−α)) in the discrete case…
A morphism is a formal arrow between two objects of a category, the basic unit of category-theoretic structure description. It is defined by a category C = (Ob, Mor, (·)∘(·), (id_A)_(A∈Ob)) in which each morphism f has a domain object A and codomain object B,…
A predictive distribution is the probability distribution p(x_new|x) over new or future data x_new, given observed data x, computed by marginalizing the likelihood p(x_new|θ) over the posterior distribution p(θ|x): p(x_new|x) = ∫ p(x_new|θ) p(θ|x) dθ. Its par…
A posterior distribution is the updated probability distribution p(θ|x) over model parameters θ after observing data x, computed by Bayes rule as p(θ|x) proportional to the likelihood p(x|θ) multiplied by the prior distribution p(θ). It encodes the full infer…
A prior distribution is a probability distribution p(θ) over the parameter space Θ of a statistical model, encoding beliefs or knowledge about θ before observing data. It is specified by the modeler and persists as a formal component of Bayesian inference, wh…
The score function U(θ;x) is the gradient of the log-likelihood with respect to the parameter, U(θ;x) = ∂/∂θ log L(θ;x), where L(θ;x) is the likelihood of parameter θ given observed data x and, for vector-valued θ, the gradient is taken component-wise. Its pa…
Pearson's chi-squared statistic is X² = Σ_i (O_i - E_i)² / E_i, a goodness-of-fit functional comparing observed category counts O_i against expected counts E_i across k categories. Its parameters are the observed counts (O_i), the expected counts (E_i, fixed…
Fisher information is a human-made measure, for a parametric statistical model, of how much information an observable random variable X (or a sample of it) carries about an unknown parameter θ governing its distribution; it is defined as the expected squared…
Conditional entropy is a human-made measure of remaining uncertainty in a random variable Y given knowledge of another random variable X. For discrete variables, H(Y|X) = -∑_x∑_y p(x,y) log p(y|x) = ∑_x p(x) H(Y|X=x). It extends Shannon entropy to the setting…
A chi-squared divergence is a human-made measure of difference between two probability distributions P and Q with densities p and q relative to a common dominating measure, defined as D_χ²(P||Q) = ∫ (p(x) - q(x))² / q(x) dμ(x) = E_Q[(dP/dQ - 1)²]. It is the f…
Kullback–Leibler divergence is a measure of how one probability distribution P diverges from a reference distribution Q. For discrete distributions: D_KL(P || Q) = Σₓ P(x) log(P(x)/Q(x)); for continuous distributions, the sum becomes ∫ p(x) log(p(x)/q(x)) dx.…
A Bayes factor is a ratio of marginal likelihoods that quantifies the evidence provided by observed data D in favor of one statistical model or hypothesis H₁ over another H₀. Given data and models M₁, M₀, the Bayes factor BF₁₀ = p(D|M₁) / p(D|M₀), where each…
A sufficient statistic is a function T(X) of a sample X such that the conditional distribution of X given T(X) carries no information about the unknown parameter θ — all inferential content about θ is contained in T alone. The identifying mechanism is the Ney…
The marginal likelihood p(x) = ∫ p(x|θ) π(θ) dθ (the model evidence) is the probability of the observed data x under a statistical model with its parameters θ integrated out against the prior π. Its parameters are the likelihood p(x|θ) with its parameter spac…
The evidence lower bound (ELBO), also called the variational lower bound or negative variational free energy, is a computable lower bound on the log marginal likelihood (log evidence) log p(x) of a Bayesian model with observed data x and latent variables z. G…
The expectation-maximization (EM) algorithm is an iterative method for finding maximum-likelihood (or maximum a posteriori) estimates of parameters θ in statistical models that depend on unobserved latent variables z. At each iteration t it alternates between…
Maximum-likelihood estimation (MLE) is a statistical method for estimating the unknown parameters θ of a fitted model from observed data x: it computes θ̂ = argmax_θ L(θ | x) = argmax_θ ℓ(θ | x), where L(θ | x) = p(x | θ) is the likelihood function and ℓ = lo…
Harmonic-to-noise ratio is a signal-level ratio HNR = 10 log10( harmonic energy / noise energy ) computed per analysis frame from a short-time spectrum, where harmonic energy is summed over identified pitch-related partials and noise energy is the residual sp…
An information criterion is a scoring rule that compares fitted statistical models by trading goodness-of-fit against model complexity: it maps a fitted model to a single number, lower values indicating the preferred model, combining the model's maximized log…
A statistical model is a mathematical construct that defines a family of probability distributions indexed by one or more unknown parameters θ, together with a specified mechanism (likelihood function) for relating observed data to those parameters. It persis…
Likelihood is a function L(θ|data) that maps each candidate parameter value θ to the probability (or probability density) of the observed data under a statistical model; it is parameterized by the data set, the probability model with its parameter space, and…
Variational inference is an approximation method for Bayesian inference that recasts posterior computation as optimization: it fixes a tractable family of distributions (the variational family, e.g. factorized Gaussians) and finds the member q* minimizing the…
The Kalman filter is a recursive optimal state estimator for dynamic linear systems with additive Gaussian noise: it represents the posterior over the hidden state as a Gaussian (mean x-hat, covariance P) and, at each step, alternates a prediction (propagatin…
state-space-model is a human-made mathematical framework for representing the evolution of a system's internal state over time using a set of first-order differential or difference equations. It expresses the system through state variables (capturing all rele…
An f-divergence is a human-made class of statistical divergences parameterized by a convex function f. For two probability distributions P, Q on the same measurable space, D_f[P||Q] = E_Q[f(dP/dQ)] where f is strictly convex with f(1)=0 and dP/dQ is the Radon…
A statistical divergence is a human-made mathematical functional D[P||Q] that maps two probability distributions P and Q on the same measurable space to a non-negative real number, with D[P||Q]=0 iff P=Q almost everywhere. Its parameters are the pair of distr…
A statistical estimator is a rule mapping a sample of observed data to an estimate of an unknown quantity. Its parameters are the sample space (the observation space from which the sample is drawn), the parameter space Θ over which the unknown quantity ranges…
Differential entropy is the extension of Shannon entropy to continuous probability distributions, defined as the negative integral of the probability density function times the logarithm of that density over the sample space; parameters are the continuous pro…
Log-likelihood is the natural logarithm of the likelihood function, which evaluates the probability of observed data given a statistical model and its parameters; it is parameterized by the data set, the probability model (including unknown parameters), and p…
Spectral flatness measure is a human-made metric that quantifies the spectral shape of a signal by comparing the geometric mean to the arithmetic mean of a power spectrum, yielding a value near zero for tonal signals and near one for noise-like signals. Param…
A statistical technique that combines predictions from multiple candidate models by computing a weighted average, rather than selecting a single best model. Given m candidate models with predictions f_i(x) and non-negative weights w_i summing to 1, the averag…
An information-theoretic criterion for statistical model selection, defined by the formula AIC = 2k − 2ln(L), where k is the number of estimated parameters in the model and L is the maximized likelihood. The criterion estimates the relative information loss w…
A probit-model is a regression technique for binary dependent variables where the latent variable y* is modeled as a linear combination of predictors (y* = Xβ + ε) with ε ~ N(0,1), and the observed binary outcome y equals 1 when y* > 0 and 0 otherwise. The pr…
minimum-phase-filter is a human-made filter class defined by the property that its phase response is the minimum possible for its magnitude response, equivalently having all zeros and poles inside the unit circle for discrete-time or in left half-plane for co…
Mel-cepstral distortion (MCD) is an objective metric that approximates the perceptual spectral difference between a reference utterance and a processed or synthesized utterance by comparing their mel-frequency cepstral coefficient vectors frame by frame. For…
A Butterworth filter is a human-made analog or digital filter design characterized by maximally flat frequency response in the passband, with no ripples. Parameters: (1) filter order N (determines rolloff steepness of 20·N dB/decade), (2) cutoff frequency fc…
A Wiener filter is a human-made optimal linear filter that estimates a desired signal from noisy observations by minimizing the mean-squared error between the estimate and the target. Parameters: (1) the signal and noise power spectral densities S_x(f), S_n(f…
The sampling theorem (Nyquist-Shannon) is a stated result of mathematical analysis: a continuous-time signal bandlimited to B hertz is completely determined, and exactly reconstructible, by its samples taken at any rate exceeding 2B hertz (the Nyquist rate),…