The accepted ontology
Browse accepted Systema Constructum entries: human-made tools, institutions, methods, practices, works, and their definitions.
100 entries in this page
Audio-watermark is a human-made data-hiding operation that embeds a robust, imperceptible payload into an audio waveform by modifying perceptually masked spectral or temporal components. It is parameterized by payload length in bits, robustness to codecs, res…
Pitch-synchronous overlap-add is a human-made time-scale modification method that aligns analysis frames to the signal's pitch periods, windows each period, and resynthesizes by overlap-add with phase continuity. Parameters include pitch period estimate, anal…
Formant warping is a human-made signal processing operation that nonlinearly maps formant frequencies between source and target vocal tracts to preserve intelligibility in voice conversion and speech synthesis. It is parameterized by a warp factor α and a fre…
Linear algebra is the branch of mathematics that studies vector spaces, linear transformations, matrices, and systems of linear equations. It provides the formal framework for representing and manipulating linear relationships through abstract algebraic struc…
Pre-emphasis is a linear filter that boosts high frequencies, typically implemented as a first-order FIR filter H(z)=1-μz⁻¹ with μ≈0.95-0.97, applied to speech signals before analysis to compensate for natural spectral roll-off and improve high-frequency repr…
Spectral magnitude is the absolute value |X(f)| of complex spectral coefficients X(f) at each frequency bin, obtained via Fourier transform or equivalent spectral decomposition of a signal. Parameters: (1) the signal representation (time-domain samples or sho…
Zero-phase filtering is a technique that eliminates phase distortion by applying a linear filter in both forward and reverse directions. The forward pass imparts phase shift φ(f); the reverse pass imparts −φ(f); the combined transfer function is |H(f)|² with…
Noise cancellation is an audio processing technique that reduces unwanted sound by generating an anti-noise signal. Active noise cancellation uses adaptive filtering to produce a signal that is the phase-inverted copy of the noise; when the two signals combin…
A linear model represents a target variable as a linear combination of predictor variables, weighted by learnable or specified coefficients. The framework takes the form y = Xβ + ε, where X is the design matrix, β the coefficient vector, and ε the error term.…
Pink noise is a class of random signals characterized by a power spectral density that decreases at 3 dB per octave (proportional to 1/frequency), meaning each octave band carries equal acoustic energy. This spectral shape makes pink noise perceptually unifor…
Spectral decay measures the rate at which spectral energy decreases over time within an analysis window. It is computed as the time constant of an exponential fit to the energy envelope of successive frequency bins, or equivalently as the difference between e…
Linear prediction estimates a signal sample as a weighted sum of previous samples: x-hat[n] equals sum of a_k times x[n-k] over prediction order k. The prediction coefficients are computed by minimizing mean squared prediction error, typically via the Yule-Wa…
Spectral manipulation is a class of signal processing techniques that operate by transforming a signal into its frequency-domain representation (typically via Fourier transform), modifying specific frequency components or spectral characteristics, and then re…
Granular synthesis is a sound synthesis technique in which an audio signal is analyzed, segmented into short overlapping fragments called grains (typically 10–100 milliseconds in duration), and then reconstructed with independent parameters controlling each g…
The discrete cosine transform (DCT) is a mathematical operation humans built to convert a finite sequence of data points into a sum of cosine functions with distinct frequencies and amplitudes. Its parameters are: input length N (power of 2 for efficient comp…
Overlap-add is a signal processing technique for reconstructing a full-length signal from overlapping, windowed segments by summing their overlapping contributions. Its parameters are: the analysis window function, the hop size (frame shift between consecutiv…
The griffin-lim-algorithm is an iterative phase reconstruction technique humans built to estimate the missing phase of a signal's short-time Fourier transform from its magnitude spectrum alone, enabling near-perfect waveform synthesis. Its parameters are: the…
Voice-activity-detection (VAD) is a binary classification technique that determines whether a given audio segment contains human speech or non-speech (silence, background noise, music). Its parameters are: the decision threshold (probability cutoff for speech…
Audio-denoising is a class of signal processing techniques that separate desired audio content from unwanted noise by exploiting differences in their statistical, spectral, or temporal properties. Its parameters are: the noise model (stationary vs. transient,…
Time-stretching is a signal processing technique that changes the duration of an audio signal while preserving its fundamental pitch. It operates by analyzing the signal into overlapping time frames, manipulating the frame sequencing (inserting or discarding…
Tonality is the system humans built to organize musical sound around a central reference pitch (the tonic), establishing hierarchies of stability among the remaining pitches and chords. Its parameters are: the tonic pitch, the scale or mode selecting which pi…
A model card is a standardized documentation artifact for machine learning models that discloses intended use, performance characteristics, training data provenance, limitations, and ethical considerations. Parameters: (1) structured sections covering model d…
Noise shaping is a digital signal processing technique that modifies the spectral distribution of quantization error by feeding the quantization error through a feedback filter. Parameters: (1) the input signal is quantized at fixed bit depth; (2) the quantiz…
White-noise is a statistical signal model characterized by equal power at all frequencies. Parameters: (1) constant power spectral density across the entire frequency range, (2) zero autocorrelation at all non-zero lags, (3) statistically independent samples…
An audio feature is a quantifiable property extracted from an audio signal that captures a specific characteristic useful for analysis, classification, or retrieval. Parameters: (1) the feature is derived from a digital audio signal through computational proc…
Spectral-whiteness is an audio analysis metric that quantifies how uniformly acoustic energy is distributed across the frequency spectrum of a signal. It measures the flatness of the power spectral density, with higher values indicating a flatter (whiter) dis…
Source-separation is a signal processing technique that decomposes a mixed signal — typically audio containing multiple overlapping sound sources — into individual component sources. The method operates by exploiting differences in spatial position, spectral…
Dither is a digital audio technique that adds a small amount of random noise (typically 1 least-significant-bit amplitude) to a signal before quantization, randomizing the quantization error and converting correlated harmonic distortion into uncorrelated nois…
Harmonic-percussive-separation is a signal processing technique that decomposes an audio signal into two additive components: the harmonic part (characterized by sustained tonal content with continuous frequency traces in the time-frequency domain) and the pe…
Phase-estimation is a class of algorithms and methods that recover the phase component of a complex signal (such as a Fourier transform) when only partial phase data or no phase data is available. It operates by imposing constraints — magnitude consistency, p…
Spectral peaks are the prominent local maxima identified within a magnitude spectrum, representing the frequency components with the highest energy density. They are computed by detecting local maxima above a noise floor threshold in the frequency domain repr…
Short-time energy is the measure of signal energy computed over a short, sliding time window (frame) in digital signal processing. It is calculated as the sum of squared amplitude values within each frame: E[n] = Σ x²[m] for m in frame n. It persists through…
Music information retrieval (MIR) is a human-made interdisciplinary field that combines signal processing, machine learning, and musicology to extract structured information from audio signals. It operates by: (1) preprocessing audio through spectral analysis…
Spectral slope is a spectral feature that quantifies the linear trend of spectral energy across frequency bins. It is computed by fitting a straight line to the magnitude spectrum across frequency using least-squares regression, and returns the slope coeffici…
A spectral transformation that remaps a linear frequency axis (Hertz) onto a non-linear perceptual frequency scale. The transformation applies a monotonic function f(frequency) where the output scale approximates human auditory perception — the mel scale uses…
Beat tracking is a music information retrieval technique that determines the temporal positions of perceptual beats in musical audio. The method operates by: (1) extracting an onset function from the audio signal, (2) computing a beat-synchronous representati…
Onset detection is a signal processing technique that identifies temporal points where acoustic events begin, by computing a feature function (typically an energy envelope or spectral flux) and locating local maxima above a dynamic threshold. The method opera…
Chroma features are a digital audio representation that projects a signal's spectral energy onto the 12 pitch classes of the Western equal-tempered scale, producing a 12-dimensional vector invariant under octave transposition. The representation is carved by…
Dynamic-range-compression is an audio processing technique that reduces the difference between the loudest and quietest parts of an audio signal. It operates by measuring the signal's amplitude envelope and applying variable gain: when the signal exceeds a th…
A mel-frequency-spectrum is a time-frequency representation that maps the linear frequency axis of a magnitude spectrum onto the mel scale — a perceptual frequency scale where equal distances correspond to equal perceived pitch intervals. It is computed by (1…
A log-magnitude-spectrum is the base-10 logarithmic transformation of a magnitude spectrum, computed as 10·log₁₀(|X(f)|²) where X(f) is the frequency-domain representation of a signal segment. It converts multiplicative convolution in the time domain (e.g. so…
A windowing function is a family of mathematical functions (e.g. Hamming, Hann, Blackman, Gaussian) that multiply a signal segment to taper its amplitude toward the edges of the analysis frame, thereby reducing spectral leakage in discrete Fourier transform a…
Pitch tracking is a signal processing technique that estimates the fundamental frequency (F0) of an audio signal as a time-varying function, producing a pitch contour. The method operates by analyzing short time frames of the audio — typically using autocorre…
The mel-frequency-cepstrum is a representation of a signal's spectral envelope warped onto the mel scale, a perceptual frequency scale where equal distances sound equally spaced to human ears. It is computed by: (1) applying a windowed Fourier transform (STFT…
Phase vocoder is a signal processing technique for modifying the duration of a signal without changing its pitch. It operates by computing the short-time Fourier transform (STFT) of the signal, manipulating the phase relationships between consecutive frames,…
Phase-recovery is the computational process of reconstructing the phase component of a signal's spectrum when only magnitude (or magnitude and partial phase) information is available. Its parameters are: (1) an input magnitude spectrum (or magnitude with inco…
A pitch-class-profile is a 12-element filter bank used to compute chroma features from a spectrogram. Each element is a kernel function (typically Gaussian) centered on the frequency of one pitch class in the 12-tone equal-tempered scale: f_c = 440 * 2^((n-69…
A chroma feature (chromagram) represents spectral energy as a 12-dimensional vector, one value per chroma (pitch class C through B), obtained by applying a pitch-class profile to a spectrogram and summing energy within each class. Computed via a 12-band filte…
The number of samples between consecutive analysis frames in windowed-overlap-add processing such as the short-time Fourier transform. It determines the overlap ratio between successive windows and controls the trade-off between time resolution and spectral s…
An iterative phase-recovery algorithm that reconstructs a time-domain signal from a magnitude spectrogram. It alternates between inverse-STFT to estimate phase, forward-STFT to enforce the magnitude constraint, and repeats until the error between the estimate…
A psychoacoustic frequency scale that maps physical sound frequency in hertz to perceived critical-band number on a 0–24 scale. The conversion is defined by the Zwicker formula: z = 13·arctan(0.00076·f) + 3.5·arctan((f/7500)^2), where z is the bark value and…
A memory encoding technique in which information is systematically associated with elements of an imagined spatial environment — a route, building, or palace. The rememberer visualizes navigating this space and encounters each designated location in sequence,…
Cepstral mean normalization (CMN) is a signal processing technique that computes the frame-wise mean of cepstral coefficient vectors across a speech utterance and subtracts this mean from each frame, thereby removing channel-induced spectral distortions and s…
Delta cepstral coefficients are computed by estimating the temporal derivative of cepstral coefficient sequences using a finite slope filter. Given a window of N cepstral frames centered at time t, the delta coefficient for each cepstral dimension d is calcul…
Spectral entropy is a scalar measure computed from the normalized power distribution across a signal's frequency bins, treating the distribution as a probability mass function and applying the Shannon entropy formula. It quantifies the uniformity of spectral…
Spectral tilt is the overall slope of a signal's power spectral density across frequency, typically expressed in decibels per octave. It quantifies how rapidly energy decreases (or increases) as frequency rises — a steep negative tilt indicates energy concent…
Fundamental frequency (F0) is the lowest frequency of a periodic waveform, representing the rate at which the sound source repeats its cycle. In speech, it corresponds to vocal fold vibration rate; in music, to the perceived pitch of tonal sounds. F0 is estim…
Phase-retrieval is the reconstruction of phase information from magnitude-only observations — an inverse problem solved by imposing constraints across domains. It operates through iterative algorithms (Gerchberg-Saxton, Griffin-Lim) that alternate between the…
Amplitude-analysis is the extraction and quantification of a signal's amplitude characteristics. It operates by computing envelope curves via rectification and low-pass filtering, measuring peak amplitudes, and deriving root-mean-square (RMS) energy values. T…
Audio restoration is the algorithmic repair of degraded audio signals. The technique analyzes corrupted audio (noisy, clipped, bandwidth-limited, or physically damaged) and applies signal processing operations — spectral subtraction, de-essing, de-clicking, e…
The constant-Q transform decomposes a signal into frequency bins whose bandwidth is proportional to center frequency, yielding a log-frequency time-frequency representation with constant quality factor Q. The analysis window length increases inversely with fr…
Mel-frequency cepstral coefficients (MFCCs) transform a signal's short-time Fourier spectrum into a compact representation of vocal tract characteristics. The process applies a mel-frequency-scale triangular filter bank to the power spectrum, computes the log…
Envelope extraction isolates the slow-varying amplitude contour of a signal by computing its short-time spectral magnitude, finding local maxima across successive frames, and smoothing the peak trajectory with a low-pass filter or moving average. It operates…
A spectral reconstruction technique takes a compact or partial spectral representation (magnitude-only spectra, quantized coefficients, or downsampled bins) and recovers a full complex-valued spectrum. It operates by iterating between spectral magnitude const…
A chroma representation (also called a chromagram) is a 12-dimensional feature vector that encodes the energy distribution across the 12 pitch classes of the equal-tempered scale (C, C#, D, D#, E, F, F#, G, G#, A, A#, B). It is computed by transforming a shor…
A parametric model is a human-made mathematical framework that represents data, signals, or phenomena using a fixed set of parameters whose values are optimized to fit observed measurements according to a specified criterion. It persists through formal algori…
A signal processing framework that represents a signal jointly in time and frequency dimensions, producing a two-dimensional distribution that reveals how spectral content evolves. It operates through parameterized transforms — short-time Fourier transform (S…
A frequency-scale is a human-made mapping function that converts a linear frequency axis to a perceptually or structurally organized scale, defined by a precise transformation formula and fixed coefficients. It persists through published standards, reference…
A frequency scale that transforms linear Hertz values to a perceptual mel scale using the formula m = 2595 × log₁₀(1 + f/700), where f is frequency in Hz. The scale approximates the human auditory system's non-linear frequency resolution and persists through…
A music-theory concept that groups all pitches sharing the same pitch name into a single equivalence class, abstracting away octave and timbre. Developed within 20th-century atonal theory (Schoenberg, Forte), it serves as the foundation for pitch-class set th…
A mathematical signal processing technique that represents a signal as a superposition of wavelets — functions localized in both time and frequency. Given a mother wavelet ψ(t), the continuous wavelet transform computes C(a,b) = ∫f(t)ψ*((t-b)/a)/√|a| dt for s…
Cepstral-distance is a measure of dissimilarity between two spectral shapes, computed from the cepstral coefficients of each spectrum. The most common form is the Itakura-Saito distance, the cepstral Euclidean distance, or the Mahalanobis distance computed on…
Linear Predictive Coding (LPC) models a digital signal (originally speech) as the output of a linear filter driven by an excitation source. For each sample s(n), the technique predicts the value as a weighted sum of p past samples: s̃(n) = Σ(aᵢ · s(n-i)) for…
A mel-spectrogram is a time-frequency representation that maps a signal's spectral energy onto the mel frequency scale, producing a 2D array with time on one axis and mel-frequency bins on the other. Parameters include: the frame size and hop length (determin…
A phoneme is the smallest abstract unit of sound in a given language such that substituting one phoneme for another in a word changes the word's meaning (minimal pair distinction). Parameters include: the language or dialect to which the phoneme system belong…
Bit-rate is the quantitative measure of the rate at which bits are processed, transmitted, stored, or generated per unit of time, expressed in bits per second (bps) and its multiples (kbps, Mbps, Gbps). Parameters include the measurement mode (instantaneous,…
A perceptual frequency scale in hertz, designed to model human auditory perception, where equal-distance steps are perceived as equal pitch intervals. The mel scale maps linear frequency f (in Hz) to perceived pitch m via the formula m = 2595 · log₁₀(1 + f/70…
Noise-reduction is a category of signal processing techniques that estimate the statistical properties of additive noise and apply a transformation to attenuate the noise component while preserving the desired signal. Key parameters: (1) noise estimation stra…
Spectral subtraction is a noise reduction technique that estimates the power spectrum of additive noise (from noise-only segments or clean speech segments), subtracts this noise estimate from the noisy signal spectrum using an over-subtraction factor, applies…
Cepstral-transform is the computational procedure that converts a time-domain signal into its cepstral representation. It operates by: (1) computing the power spectral density of the input signal via FFT, (2) taking the logarithm of the spectrum, and (3) appl…
Liftering is a signal processing technique that applies a window function to the cepstrum in the quefrency domain to selectively modify frequency components. Procedure: compute cepstrum via FFT of log-power spectrum; multiply cepstrum by a window function (lo…
Cepstral coefficients are a representation of the spectral envelope of a signal, obtained by applying a discrete cosine transform to the log power spectrum. They are computed in three stages: (1) compute the power spectrum via Fourier transform, (2) take the…
Pitch-detection is a computational technique that estimates the fundamental frequency (F0) of a periodic or quasi-periodic signal, most commonly audio or speech. Parameters: (1) input signal — the waveform or its spectral representation (STFT, cepstrum, or ra…
Furniture comprises human-made, movable objects designed to support specific human activities — sitting, sleeping, storing, working, eating — through engineered form-function relationships. Parameters: (1) a physical artifact designed for human use rather tha…
Spectral-feature is a numerical descriptor extracted from a signal's spectral representation that captures a measurable aspect of its frequency-domain structure. Parameters: (1) source domain — the spectral representation from which the feature is derived (po…
A cepstral lifter is a filter operating in the quefrency (cepstral) domain. Parameters: (1) lifter type — low-pass (extracts spectral envelope by preserving low-quefrency coefficients), high-pass (extracts residual/excitation by preserving high-quefrency coef…
Short-Time Fourier Transform (STFT) is a time-frequency analysis technique. Parameters: (1) window size — the length of each segment in samples; (2) window type — the tapering function (Hann, Hamming, Blackman, etc.) applied to reduce spectral leakage at segm…
Spectral decomposition is a mathematical technique that represents a signal or function as a sum of basis functions indexed by frequency. The input is a time-domain or spatial-domain signal x(t); the output is a frequency-domain representation X(f) where each…
The discrete-cosine-transform (DCT) is a linear invertible transform that maps a real-valued input sequence x[n] of length N into real-valued coefficients X[k] via the formula X[k] = sum_{n=0}^{N-1} x[n] * cos(pi/N * (n + 0.5) * k), for k = 0..N-1. It comes i…
Frequency warping is a technique in audio signal processing that transforms frequencies from one scale to another through a monotonic mapping function. The most common form maps physical frequencies in hertz to perceptual frequency scales such as the mel scal…
A mel-frequency scale is a perceptual frequency scale used in audio signal processing and psychoacoustics that approximates human pitch perception. It maps physical frequency in hertz to mel units using the transformation: mel = 2595 × log₁₀(1 + f/700), where…
A cross-correlation is a mathematical operation that computes the similarity between two signals x(t) and y(t) as a function of a time lag τ applied to one signal: R_xy(τ) = ∫ x(t)·y*(t-τ) dt (continuous) or R_xy[τ] = Σ x[n]·y*[n-τ] (discrete). It operates by…
A mel-frequency-spectrogram is a time-frequency representation of a signal constructed in three steps: (1) partition the signal into overlapping frames using a window function, (2) compute the periodogram (or Welch estimate) for each frame to obtain a linear-…
A spectral peak is a local maximum in the magnitude spectrum of a signal — a frequency bin whose spectral amplitude exceeds that of its neighboring bins above a specified threshold. The parameters that carve a spectral peak are: (1) a spectral representation…
Cepstral-envelope is the slowly-varying amplitude profile extracted from cepstral coefficients by applying low-pass liftering (quefrency-domain windowing). It captures the gross spectral shape of a signal — notably the vocal tract characteristic in speech — b…
A spectrum-analyzer is a measurement instrument that converts a time-domain input signal into its frequency-domain representation, displaying amplitude (or power) as a function of frequency. It operates by either (1) sweeping a tunable band-pass filter across…
A band-pass-filter is a signal processing construct that passes signals within a specific frequency range (defined by a lower cutoff frequency f_L and an upper cutoff frequency f_H) while attenuating frequencies outside that band. Its behavior is fully specif…
A filter-bank is a human-made signal processing construct consisting of a parallel array of band-pass filters, each tuned to a distinct frequency band, that decompose an input signal into its constituent spectral components by routing each band through its de…
A nyquist-frequency is the theoretical upper bound on signal frequency that can be unambiguously represented after sampling at a given rate, defined as exactly half the sampling rate (fs/2). Frequencies above this bound fold back into the representable range,…
A bartlett method is a spectral estimation technique that computes a smoothed power spectrum estimate by partitioning a finite-length discrete signal into M non-overlapping segments of equal length L, computing the periodogram for each segment via magnitude-s…