The accepted ontology
Browse accepted Systema Constructum entries: human-made tools, institutions, methods, practices, works, and their definitions.
100 entries in this page
A welch-method estimate of a signal's power spectral density is produced by dividing a finite-length discrete signal into M non-overlapping (or optionally overlapping with 50% overlap) segments of equal length L, applying a window function (typically Hann or…
A spectral-estimation technique infers the frequency-domain structure (power spectral density or amplitude distribution across frequencies) of a signal from a finite set of time-domain samples. It takes measured data — a discrete sequence of N samples — and m…
A periodogram is a spectral estimation technique that computes the squared magnitude of the discrete Fourier transform of a signal to estimate its power spectral density. It converts a time-domain signal into a frequency-domain representation showing how the…
Power spectral density (PSD) is a spectral representation that quantifies the distribution of signal power across frequency. Computed via the Fourier transform of the autocorrelation function (Wiener–Khinchin theorem) or estimated from finite data using perio…
Spectral-energy is the total power or energy of a signal computed by integrating its power spectral density across all frequency components within a given analysis window. It is quantified as the sum of squared amplitude values across the spectrum, providing…
Spectral representation is a mathematical encoding of a signal's frequency-domain structure. Its parameters are: (1) the input signal s(t) in the time domain, (2) the transform kernel K(f,t) that maps time to frequency (e.g., complex exponential for Fourier t…
Mel spectrum is the spectral representation of a signal obtained by applying a mel-scale triangular filterbank to its power spectrum. Its parameters are: (1) the input power spectrum P(f) giving energy at each linear frequency bin, (2) the mel filterbank matr…
Spectral bandwidth is the weighted standard deviation of frequency bins around the spectral centroid, computed from the power spectrum of a signal. Its parameters are: (1) the power spectrum P(k) giving magnitude at each frequency bin k, (2) the spectral cent…
Spectral rolloff is an audio signal processing feature that computes the frequency below which a specified percentage (commonly 85%) of the total spectral energy is concentrated. It operates by accumulating spectral magnitude values in descending frequency or…
Spectral contrast is a signal processing feature that quantifies the tonal contrast of a frequency spectrum. It computes the difference between peak and valley energy values within user-defined frequency bands of a power spectrum, producing a vector of contra…
Cepstral subtraction is a speech enhancement technique that reduces additive noise by operating in the cepstral domain. Introduced by Boll (1979), it works by computing the cepstrum of a noisy speech frame, identifying the quefrency range where noise dominate…
Homomorphic filtering is a signal processing technique that decomposes a signal into convolutional or multiplicative components by mapping it into a domain where these operations become additive. The method applies three steps: (1) take the logarithm of the s…
Spectral-flatness is a signal processing feature that quantifies how sinusoidal (tonal) versus noise-like a power spectrum is. It is computed as the ratio of the geometric mean to the arithmetic mean of the spectral power values across frequency bins. Paramet…
Spectral flux is a signal processing feature that quantifies the rate of change of the power spectrum over time. It operates by computing the power spectral density within successive overlapping windows and measuring the L1 distance (sum of absolute differenc…
Zero-crossing-rate (ZCR) is the count or normalized rate of sign changes in a discrete-time audio signal within a defined analysis window. The parameters are: (1) the window size (typically 20-40ms for speech), (2) the window function applied before counting…
Cepstral-liftering is a signal processing technique that applies a window-like function in the cepstral domain to selectively smooth or accentuate cepstral coefficients. It operates by applying a lifter (a low-pass, high-pass, or band-pass filter) to the ceps…
Speech-recognition is the human-made methodology and system for converting spoken language into text or structured representations through signal processing, linguistic modeling, and pattern classification. The concept carves a pipeline: audio capture → featu…
Harmonic is the human-made concept designating a tone whose frequency is an exact integer multiple of a fundamental frequency (n×f₀, n∈ℕ⁺). The concept carves a discrete set of frequency relationships that define timbre in acoustics, govern instrument resonan…
A mel-filter-bank is a set of triangular overlapping filters spaced according to the mel scale, applied to a power spectrum or spectral representation to extract energy in perceptually-relevant frequency bands. Parameters: number of filters (typically 20-40),…
Mel-scale is the human-made perceptual frequency scale used in audio and speech processing. It maps linear Hertz frequencies to a scale where equal distances sound equally distant to human listeners. Construction: m = 2595 × log₁₀(1 + f/700), where f is frequ…
Cepstral-domain is the human-made mathematical representation space in which cepstral coefficients are defined and manipulated. Constructed by: (1) computing the power spectrum of a signal via FFT; (2) taking the natural log of each frequency bin's magnitude;…
Mfcc (mel-frequency cepstral coefficients) is the human-made feature extraction technique that converts audio signals into a compact set of coefficients representing the short-term power spectrum envelope. Procedure: (1) frame the signal into overlapping wind…
Statistical-analysis is the human-made methodological framework for collecting, examining, and interpreting data using mathematical-statistical techniques to extract meaning, discover patterns, and support inference. It operates through a defined pipeline: sp…
A cepstrum-coefficient is the individual amplitude value obtained at a specific quefrency from the cepstrum computation: the inverse Fourier transform of the logarithm of a signal's power spectrum. Each coefficient corresponds to one quefrency point and encod…
Signal-to-noise ratio (SNR) is a dimensionless quantitative measure that compares the power level of a desired signal to the power level of background noise. It is defined as SNR = P_signal / P_noise, where P denotes average power. In decibels: SNR(dB) = 10·l…
The discrete Fourier transform (DFT) is a mathematical algorithm that converts a finite sequence of N time-domain samples into a finite sequence of N frequency-domain complex coefficients. It computes X[k] = sum_{n=0}^{N-1} x[n] * exp(-2*pi*i*k*n/N) for k = 0…
Signal-processing is the human-made discipline of analyzing, modifying, and synthesizing signals — mathematical representations of information carried by measurable quantities — to extract meaning, compress data, detect patterns, or produce desired outputs. I…
Arithmetic is the branch of mathematics concerned with the operations on numbers and the study of properties of certain algebraic structures arising from addition, subtraction, multiplication, and division. It operates through formal rules governing numerical…
Cepstral analysis is the signal processing technique that transforms a signal's spectral representation into the quefrency domain by computing the inverse Fourier transform of the logarithm of the magnitude spectrum. The method operates on the principle that…
The magnitude spectrum of a signal is the function mapping each frequency to the amplitude (modulus) of the corresponding complex-valued spectral coefficient from a frequency-domain transform (Fourier, Laplace, or Z-transform). It records the energy distribut…
The phase spectrum of a signal is the function that assigns, to each frequency component in a spectral decomposition, the phase angle (argument) of the corresponding complex-valued spectral coefficient. It is obtained by applying a frequency-domain transform…
A cepstral coefficient is a single value in the cepstrum sequence, representing one spectral envelope feature extracted from the logarithm of a power spectrum. Cepstral coefficients are computed by: (1) computing the power spectral density of a signal, (2) ta…
A time-frequency representation (TFR) is a signal-processing technique that maps a one-dimensional time-domain signal into a two-dimensional representation showing how frequency content varies over time. Unlike the Fourier transform, which collapses all tempo…
Quefrency is a human-made variable introduced with cepstral analysis to name the independent axis of the cepstrum — it measures periodicity in a frequency spectrum, expressed as a 'reverse time' whose units match those of the original domain (e.g., millisecon…
The short-time Fourier transform (STFT) is a signal-processing procedure that partitions a signal into short, overlapping time windows using a window function (e.g., Hann, Hamming, or Gaussian), computes the discrete Fourier transform of each windowed segment…
A spectrogram is a visual display that maps signal energy across frequency and time, produced by computing successive short-time Fourier transforms with a defined window size and overlap, then rendering the resulting magnitude spectrum as a color- or intensit…
Deconvolution is a signal processing technique that recovers an estimate of an original source signal from an observed signal degraded by convolution with a known kernel. Given an observed signal y = x * h (where * denotes convolution and h is the known point…
A cepstrum is a signal processing transform that maps a power spectrum into a quefrency domain by applying the inverse Fourier transform to the logarithm of the power spectrum. The procedure: (1) compute the power spectrum of a signal via FFT, (2) take the na…
The spectral centroid is a human-made measure used in signal and audio processing that quantifies the 'center of mass' of a spectrum's magnitude distribution — the point at which the energy of the spectrum would balance if it were a physical object. It is com…
Spectral-resolution is the human-made parameter that quantifies the minimum frequency separation required to distinguish two distinct spectral components as separate peaks in a frequency-domain representation of a signal. It is determined by the analysis meth…
Filter-design is the structured practice of creating filters — systems that shape the frequency content of signals by attenuating unwanted bands and preserving desired ones. It operates by specifying target frequency-response characteristics (passband, stopba…
The Laplace transform is a mathematical operation that maps a function of time (typically a real variable t ≥ 0) to a function of a complex variable s = σ + jω, defined as the integral F(s) = ∫₀^∞ f(t)e^(-st) dt. It carves the transform as a generalization of…
The phase response is a human-made concept in signal processing that specifies how different frequency components of a signal are shifted in phase by a linear system. It is the angular component of the complex frequency response H(ω) = |H(ω)|·e^(jφ(ω)), where…
The linearity is a human-made concept describing a class of systems whose behavior satisfies two properties: homogeneity (scaling the input scales the output by the same factor) and superposition (the response to a sum of inputs equals the sum of individual r…
The ringdown is a human-made concept describing the gradual decay of oscillatory motion in a physical or engineered system after the excitation force is removed. It is characterized by two parameters: the decay rate (determined by the system's damping coeffic…
The spectral analysis is a human-made practice for decomposing a signal into its constituent frequency components and examining how energy, amplitude, and phase are distributed across those frequencies. It operates by applying a mathematical transform — most…
The hamming window is a human-made mathematical function used in signal processing to taper signals before spectral analysis. It is defined by the formula w(n) = 0.54 - 0.46*cos(2*pi*n/(N-1)) for n in [0, N-1], where N is the window length. Its parameters are…
Transient response is the time-domain behavior of a system following a sudden change (step, impulse, or pulse) in its input. It comprises three phases: initial reaction (rise time and overshoot), oscillatory behavior (ringing at the system's natural or resona…
The Fourier transform is a human-made mathematical framework that maps a function (typically a signal in time domain) into a representation in terms of its constituent frequencies. It operates by applying an integral kernel e^(-jωt) to decompose functions int…
Spectral density quantifies how signal power or energy is distributed across frequency. For deterministic signals, the energy spectral density is the squared magnitude of the Fourier transform; for stochastic processes, the power spectral density is the Fouri…
Frequency resolution is the minimum frequency separation at which two sinusoidal components can be distinguished as separate peaks in a spectral estimate. For the DFT with N samples at sampling rate fs, the bin spacing is fs/N; effective resolution is worsene…
Power spectrum quantifies the distribution of signal power across frequency, showing which frequency bands carry the most energy. For deterministic energy signals, it is computed as the squared magnitude of the Fourier transform |X(f)|²; for stochastic power…
An anti-aliasing filter is a low-pass signal-processing circuit or algorithm applied before the sampling stage of an analog-to-digital conversion. It attenuates frequency components above the Nyquist frequency (half the sampling rate) to prevent higher-freque…
Zero-padding is a signal-processing technique in which zeros are appended to a finite discrete-time signal before computing its Discrete Fourier Transform (DFT). The operation does not add information to the signal but interpolates the spectral estimate by in…
The Nyquist criterion is a theorem in signal processing that establishes the minimum sampling rate required for perfect reconstruction of a continuous-time signal. It states that the sampling rate fs must satisfy fs > 2·fmax, where fmax is the highest frequen…
A window function is a mathematical function that assigns a smoothly decaying weighting to the samples of a finite data segment, effectively tapering the signal amplitude toward zero at the boundaries. It is applied before a Fourier transform to minimize spec…
Aliasing is the error artifact that occurs when a continuous signal is sampled at a rate below twice its highest frequency component (the Nyquist criterion), causing frequency components above the Nyquist limit to fold back and appear as spurious lower-freque…
The sinc function is the mathematical function sinc(x) = sin(πx)/(πx), defined piecewise with sinc(0) = 1 by continuity. It is a cornerstone of Fourier analysis, appearing as the Fourier transform of the rectangular window and as the impulse response of an id…
Ringing is the concept of sustained oscillations that persist in a dynamic system's output after a transient disturbance has ended. It manifests when a system with overshoot exhibits underdamped behavior, causing the response to oscillate around the steady-st…
Spectral leakage is the human-made phenomenon where the finite observation of a signal causes its frequency spectrum to spread beyond the true frequency components, producing artificial side-lobes. It arises from the implicit rectangular-window multiplication…
Reactance is the imaginary component (X) of complex impedance in AC circuit analysis, quantifying opposition to sinusoidal current arising from energy storage rather than resistive dissipation. Parameters: (1) inductive reactance X_L = ωL (positive, from indu…
Windowing is a human-made technique in signal processing that multiplies a signal segment by a mathematical window function to reduce spectral leakage during Fourier analysis. Parameters: (1) window shape (Hann, Hamming, Blackman, Kaiser, or custom) determini…
Impedance is the complex-valued measure of opposition that a circuit element or network presents to sinusoidal current at a given frequency. Parameters: (1) resistance R (real part, frequency-independent opposition from dissipation), (2) reactance X (imaginar…
A frequency-response is the characterization of how a system's output magnitude and phase vary as a function of sinusoidal input frequency. Parameters: the independent variable is frequency (typically spanning DC to the system's bandwidth); the dependent vari…
Step-response is the temporal output of a system following a step input — an instantaneous transition from one constant amplitude level to another. The step-response characterizes a system's transient behavior including rise time, settling time, overshoot, an…
Group-delay is a human-made analytical concept in signal processing and wave physics that quantifies the time delay experienced by the envelope of a signal's spectral components as they pass through a system. Parameters: (1) the group-delay function τ_g(ω) =…
Bandwidth is the span of frequencies over which a system, device, or signal operates within specified performance bounds. It is carved by three parameters: (1) the frequency range [f_low, f_high] that defines the passband or operational band, (2) the acceptan…
A phase-shift is a deliberate displacement of the timing alignment of a periodic waveform relative to a reference point, quantified in angular measure (degrees or radians). It is carved by three parameters: (1) the reference signal against which displacement…
A filter is a signal-processing construct that selectively passes or attenuates frequency components of a signal based on a designed transfer function. It operates by applying a frequency-dependent modification — such as low-pass, high-pass, band-pass, or not…
Overshoot is a quantifiable metric in signal processing and control theory that measures the maximum percentage by which a system's step response exceeds its final steady-state value before settling. It is defined mathematically as the ratio of (peak response…
A phasor is a human-made representational construct in electrical engineering and signal processing that encodes a sinusoidal steady-state signal as a single complex number, capturing amplitude and phase while suppressing the implicit carrier frequency and ti…
A convolution is a mathematical operation that combines two functions to produce a third, expressing how the shape of one is modified by the other. Parameters: (1) domain — continuous (integral form: ∫f(τ)g(t-τ)dτ) or discrete (summation form: Σf[k]g[n-k]); (…
Dissipation is the irreversible loss of organized energy into disordered thermal motion within a physical or engineered system. Parameters: (1) rate — the power of energy loss per unit time, quantified by dissipation function or damping coefficient; (2) mecha…
The amplitude-envelope is a formal model of how the magnitude (amplitude/loudness) of a sound or signal evolves over time. Parameters: (1) temporal trajectory — the amplitude value as a function of elapsed time since onset; (2) characteristic points — attack…
The impulse-response is the complete characterization of a linear time-invariant (LTI) system given by its output when the input is a Dirac delta function — an idealized infinitesimally-brief unit pulse. Parameters: (1) the impulse-response function h(t) in t…
The attack is the initial phase of a sound's amplitude envelope — the time interval and trajectory from silence to peak amplitude when a sound begins. Parameters include attack time (duration from onset to peak) and attack slope (rate of amplitude rise). The…
Phase is the human-made concept of a point within the cycle of a periodic waveform, quantified as an angle (radians or degrees) or fraction of a complete period. It parameterizes the relative timing between oscillating quantities, enabling precise description…
The Discrete Fourier Transform (DFT) is a mathematical transformation that maps a finite sequence of N time-domain samples x[0], ..., x[N-1] to a finite sequence of N complex frequency-domain coefficients X[0], ..., X[N-1], computed by the formula X[k] = Σ(n=…
The Fast Fourier Transform (FFT) is an algorithm that computes the Discrete Fourier Transform (DFT) of a sequence, or its inverse (IDFT). It transforms a finite sequence of equally-spaced samples of a function from its time-domain representation to its freque…
Transient is the concept of a brief, short-duration phenomenon — specifically in acoustics and audio processing, it names the initial attack phase of a sound characterized by rapid amplitude rise and high energy concentration before the steady-state or sustai…
Damping is the concept of controlled energy dissipation in an oscillating system — the introduction of a resistive force proportional to velocity that reduces amplitude over time. It is parameterized by the damping ratio (underdamped, critically damped, overd…
Amplitude is the concept of maximum displacement from equilibrium in an oscillating or wave system — a quantitative measure of the strength or intensity of a wave, signal, or periodic phenomenon. It applies to mechanical waves (sound, water), electromagnetic…
Loudness is the perceptual correlate of acoustic stimulus intensity — the subjective magnitude with which a listener experiences sound pressure. It is not identical to sound pressure level (SPL); rather, loudness is the mind's mapping of physical amplitude on…
Onset is the human-constructed concept marking the temporal beginning — the attack phase — of a sound event. It identifies the transition from silence or non-sound to audible sound, and is used extensively in acoustics, music perception, and speech analysis (…
A formant is a resonant frequency band of the vocal tract — a peak in spectral energy produced when the vocal tract acts as an acoustic filter, amplifying harmonics at specific frequencies. Formants are determined by the shape and size of the vocal tract cavi…
Harmonics are the integer-multiple frequencies produced by a vibrating system alongside its fundamental. Parameters: the fundamental frequency f₀, the harmonic series (n·f₀ for n=1,2,3,...), and the amplitude envelope across partials. Persistence: sustained t…
Phrase is the human-constructed concept of a group of words forming a single unit of meaning within a larger syntactic structure. It is bounded by syntactic boundaries (not necessarily sentence boundaries), carries coherent semantic content, and functions as…
A waveform is the mapping of a signal's amplitude (or other varying quantity) onto a temporal axis, producing a shape that encodes the signal's morphological properties. Its parameters are: the dependent variable (amplitude, pressure, voltage), the independen…
Spectral envelope is the human-constructed concept describing the overall shape of a sound's frequency spectrum — which frequency bands are amplified or attenuated relative to others. It is the macroscopic profile carved by the combined resonant and anti-reso…
Interval is a human-made musical concept that names, measures, and classifies the distance between two pitches within a given tuning system. Its parameters are: (1) step count — the number of scale degrees separating the two notes; (2) quality classification…
Tuning is the practice of establishing and maintaining standardized pitch relationships within a musical system. Its parameters are: (1) reference pitch — a fixed frequency assigned to a named note (e.g. A4=440 Hz), (2) temperament — the system of interval si…
Flow is a psychological state of deep, focused engagement in an activity, characterized by five operational parameters: (1) intense concentration on the present moment — attention narrows to activity-relevant stimuli, (2) merging of action and awareness — doi…
Melody is a sequence of pitched notes arranged in time to form a coherent musical unit. Its parameters are: (1) pitch succession — notes ordered by frequency, (2) temporal organization — notes arranged in a specific rhythm and duration, (3) contour — the over…
Frequency is the count of recurring events per unit of time, expressed as cycles, oscillations, or vibrations per second (hertz). It quantifies periodicity by measuring how often a repeating pattern completes in a given interval. Parameters: measurable rate o…
Polyphony is the compositional practice of combining two or more independent melodic voices into a single simultaneous texture. Parameters: (1) the minimum number of voices is two (dyadic polyphony); (2) each voice maintains melodically independent contour an…
Pitch is the perceptual attribute of sound that allows auditory experiences to be ordered on a frequency-related scale from low to high. Parameters: (1) the physical stimulus is a periodic sound wave characterized by a fundamental frequency measured in Hertz;…
Equilibrium is a state in which competing forces, influences, or tendencies are balanced such that no net change occurs. It has two forms: static equilibrium (forces cancel completely, producing rest) and dynamic equilibrium (opposing flows maintain a steady…
A spectrum is an analytical representation that maps a measured or computed quantity (amplitude, power, intensity) to a domain variable (frequency, wavelength, energy, mass). Parameters: (1) the domain axis, which determines the type of spectrum (e.g. frequen…
A harmonic series is the ordered sequence of frequencies f_n = n × f_0 where f_0 is a fundamental frequency and n ranges over positive integers (1, 2, 3, ...). Parameters: (1) each member is an exact integer multiple of the fundamental; (2) the sequence is or…
An overtone is any frequency component of a complex sound that exceeds the fundamental frequency. Parameters: (1) it must be a component of a harmonic or inharmonic complex tone; (2) its frequency is strictly above the fundamental. Persistence: the concept pe…