spectral-representation

Spectral representation (expressing a signal in terms of its frequency components) is a specific type of representation — it maps a signal's time-domain content into a frequency-domain symbolic form. Per Law 9: specific→general INSTANCE_OF. Nearest kind is representation (the broader concept of encoding information in a different form).

Spectral representation describes signal properties as functions of frequency. Remove frequency and the concept of spectral representation has no meaningful domain — the frequency axis IS the representation. Removal test passes: without frequency, spectral representation stops operating.

Spectral bandwidth measures the range of frequencies covered by a spectral representation. Remove the spectral representation and there is no spectrum to measure bandwidth across — the concept of spectral bandwidth loses its referent. Present-tense dependency.

A power spectrum is a specific type of spectral representation that shows the distribution of signal power across frequency. 'Power spectrum is a spectral representation' — a competent speaker would call X a Y. Files against nearest kind per Law 11.

The cepstrum is a specific type of spectral representation: it displays signal characteristics as amplitude versus quefrency (the frequency-like domain of the cepstral transform). A competent speaker would call it a spectral representation. This files against the nearest kind — spectral-representation, not the more general power-spectrum.

The mel-spectrum is a specific type of spectral representation: it displays signal power distributed across the mel frequency scale (a perceptual frequency scale). A competent speaker would call it a spectral representation. This edges mel-spectrum to its nearest kind.

Spectral-energy IS a specific kind of spectral representation: it presents signal energy as a function integrated over frequency within an analysis window. A competent speaker would call spectral energy a spectral representation. Files against nearest kind in the spectral analysis hierarchy.

Spectral bandwidth was derived from spectral representation — the concept of measuring frequency spread only makes sense after spectral representations existed. Spectral bandwidth measures the spread of frequencies within a spectral representation, which historically followed and conceptually depends on the prior existence of spectral representation as a concept.

DERIVED_FROM is not applicable here — this is INSTANCE_OF. power-spectral-density IS a specific kind of spectral representation: it presents signal power as a function of frequency. A competent speaker would call PSD 'a spectral representation'. Files against the nearest kind.

A spectral-envelope IS a specific kind of spectral-representation. It represents the smooth, coarse shape of a spectrum, filtering out fine structure and harmonic detail. A competent speaker would call it 'a spectral representation' — it represents spectral energy distribution, albeit in a smoothed form. Files against the nearest kind.

Spectral decomposition IS a form of spectral representation — it represents a signal as a decomposition into frequency components. This is the nearest kind for spectral-decomposition.

Cepstral-coefficients IS a specific kind of spectral-representation. It represents the spectral content of a signal in the quefrency domain — a transformation of the frequency-domain representation. A competent speaker would call cepstral coefficients 'a spectral representation.' Nearest kind check: spectral-representation is not already reached via an accepted INSTANCE_OF ladder from cepstral-coefficients.

Log-magnitude-spectrum is a specific kind of spectral representation obtained by applying a logarithmic transform to spectral magnitudes. A competent speaker calls it a type of spectral representation. Specific→general per Law 9. Nearest kind is spectral-representation (Law 11e).

magnitude-spectrum is a specific kind of spectral-representation: it represents signal energy across frequency using raw (or log) magnitude values. A competent speaker would call it 'a spectral representation'.

Chroma features operate by projecting a signal's spectral representation onto pitch-class bins. Remove spectral-representation as input and chroma-features have no data to operate on — the projection target is the spectral energy distribution, which IS a spectral representation. This is a present-tense constitutive dependency.

Mel-frequency spectrum is a specific kind of spectral representation that maps the frequency axis onto a perceptual mel scale. A competent speaker would call MFCC 'a spectral representation.' Files against nearest accepted kind.

A spectrogram is a specific kind of spectral-representation — it represents the time-varying frequency content of a signal as a 2D visual/tablature display (time vs frequency, color-coded by magnitude). A competent speaker would call a spectrogram a spectral representation. The edge points specific→general.

Spectral slope measures the tilt/gradient of a spectrum's energy distribution. Which-came-first: spectral representations (Fourier analysis) existed first, and spectral slope was derived as a feature computed from them. Spectral representations are the source concept.

Mel-filterbank operates on a spectral representation as its input data. Remove spectral-representation (the frequency-domain data structure) and the mel-filterbank has no data to filter — the removal test passes. The triangular weighting is applied to spectral bins.

Freq-warping remaps frequencies on a spectral representation (e.g., linear to mel scale). Remove spectral-representation and freq-warping has no data to warp — the removal test passes. The operation is defined entirely in terms of transforming spectral bins.

Chroma IS a specific kind of spectral representation — it represents the spectral energy distributed among octaves/pitch classes. A competent speaker would call chroma 'a spectral representation.' Files against the nearest kind.

Spectral decay operates on spectral energy values extracted from a spectral representation. Remove spectral representation and spectral decay has no input data to operate on — the feature cannot be computed. Present-tense constitutive dependency, not historical association.

A spectral peak identifies the frequency bin with maximum energy within a spectral representation. Remove spectral representation and spectral peak has no data to analyze — it is an operational dependency, not just an association.

Spectral manipulation operates ON a spectral representation — it modifies, transforms, or processes spectral data. Remove spectral representation as a concept and spectral manipulation has no domain to act upon. The removal test passes constitutively: manipulation requires a representation to manipulate.

Formant warping requires a spectral representation (magnitude spectrum) to operate — it warps spectral peaks non-linearly. Remove spectral-representation and there is nothing to warp. Per Law 8 removal test: DEPENDS_ON.

Spectral coloration is the property of uneven energy distribution in a spectrum. It is a property OF a spectral representation — the concept depends on spectral representation existing as the carrier concept. Remove spectral representation and 'spectral coloration' has nothing to be a property of.

DFT is a specific computational method for producing a spectral representation. Which came first? The general concept of representing signals in the frequency domain (spectral representation) predates the specific algorithm (DFT). spectral-representation=0.03, DFT=0.06 → spectral-representation is older and more general.

Spectral whitening operates directly on spectral representations (magnitude spectra from DFT/FFT). It flattens the spectral envelope by dividing the spectrum by its estimated envelope. Remove spectral-representation and spectral whitening has no data to operate on — the technique IS a manipulation of spectral representations. The removal test passes.

Audio compression algorithms (MP3, AAC, Opus) use spectral-representation — transforming time-domain audio into frequency bins via FFT/MDCT — as their fundamental analysis step. The perceptual model that determines what to quantize/ discard operates on the spectral representation. Remove spectral-representation and the compression algorithm has no framework for psychoacoustic masking or frequency-domain quantization. Present-tense dependency per Law 8.

HPSS decomposes audio into harmonic and percussive components using time-frequency median filtering on the spectrogram — a spectral representation derived from STFT. Remove spectral-representation and the median filtering of magnitude spectra has no input to operate on. Present-tense dependency per Law 8.

Spectral flattening operates on the magnitude spectrum of an audio signal — a spectral representation obtained via FFT or similar transform. It applies an inverse filter to the spectral envelope. Remove spectral-representation and the flattening algorithm has nothing to operate on. Present-tense dependency per Law 8.

Spectral-flatness (the ratio of geometric to arithmetic mean of a power spectrum) is a metric derived from spectral representation. Remove spectral-representation and the concept of spectral-flatness ceases to have meaning. Epoch test confirms: spectral-flatness (0.71) is newer than spectral-representation (0.03).