spectral-centroid

Spectral centroid is computed from a frequency spectrum, which comes from the Fourier transform. Remove FT and you lose the spectrum entirely — spectral centroid ceases to operate. Direction tested: fourier-transform existed first, and spectral-centroid depends on having spectral data from it.

Spectral centroid is the weighted average of frequency components in a spectrum, a concept that fundamentally derives from frequency as a measurable quantity. Frequency as a concept predates spectral centroid and is the substrate upon which spectral centroid is built.

Spectral centroid is a spectral feature computed to serve analysis — it represents the center of mass of a spectrum, used in audio and signal analysis to characterize timbre and spectral shape. Remove analysis as its purpose and it has no standalone function. Its designed purpose is to further analytical understanding of signals.

Spectral centroid is computed from the magnitude spectrum: it is the center of mass of the spectrum, calculated as the weighted average of frequencies using magnitudes as weights. Magnitude spectrum existed first as a representation; spectral centroid is derived from it. Which came first? The magnitude spectrum representation predates the centroid statistic.

Spectral centroid is computed as the center of mass of the magnitude spectrum — a weighted average of frequencies using magnitudes as weights. Remove the magnitude spectrum and spectral centroid computation stops operating entirely. Law 8 present-tense removal test passes.

Spectral-centroid is computed as the weighted mean frequency of the power spectrum: Σf·P(f)/ΣP(f). Remove the power-spectrum concept and the spectral-centroid cannot be computed — it is literally the center-of-mass of the power spectrum. The removal test passes: no power-spectrum, no spectral-centroid.

Spectral-centroid IS a specific kind of spectral feature: it measures the 'center of mass' of a spectrum, representing the perceptual brightness of a sound. A competent speaker classifies it as 'a spectral feature'.

spectral-centroid computes the weighted mean frequency of the spectrum. It directly operates on the power spectrum — remove spectrum and centroid has no input. Genuine operational dependency.

Spectral centroid is the weighted mean frequency of a spectrum, computed from the magnitude spectrum produced by STFT. Remove STFT and the magnitude spectrum — and thus the centroid — cannot be computed.

Spectral centroid is a specific measurement of the spectral center of gravity of a signal; a competent speaker would call it a measurement of timbre.

Spectral centroid is built for the sake of timbre characterization — it provides a single number summarizing spectral shape, used to estimate perceived timbre brightness. Purpose is timbre analysis, Law 8d.

Spectral centroid is a specific signal processing technique that computes the weighted mean of frequencies present in a signal spectrum, producing a single number summarizing spectral shape. A competent DSP practitioner would classify spectral centroid as a signal processing method. Specific to general, Law 9.

Spectral-bandwidth measures the spread of frequencies around the spectral-centroid. The centroid is the reference point — bandwidth = spread from centroid. Remove spectral-centroid and bandwidth loses its anchor concept. Law 8 removal test passes.