frequencyare

Frequencyare is a proposed metric in signal analysis intended to quantify how a signal's frequency content is distributed over time. It provides a compact, scalar representation of spectral density within a specified frequency range, combining temporal dynamics with spectral information. In this framework, higher frequencyare values indicate relatively more energy concentrated at higher frequencies, while lower values indicate dominance of lower frequencies.

Etymology and Concept: The term frequencyare blends frequency and area, reflecting the idea of an area-normalized density of spectral energy. It is not part of standard terminology and is primarily used in theoretical discussions or exploratory data analysis to compare timbral or spectral complexity across signals.

Estimation: In practice, one computes a time-varying spectrum S(t,f) via a time-frequency transform such as the STFT or a wavelet transform. A simple estimator defines the unnormalized first moment m1(t) = ∫ f S(t,f) df over a chosen band [f_min, f_max], and the energy E(t) = ∫ S(t,f) df. The frequencyare is then the dimensionless quantity A(t) = [m1(t) - f_min] / (f_max - f_min), or equivalently A(t) = (normalized mean frequency within the band).

Relation and limitations: Frequencyare relates to established measures such as spectral centroid, spectral shape metrics, and time-frequency energy distribution. It is sensitive to the chosen frequency band and time window, and may be affected by noise or windowing effects. Because it collapses a time-varying spectrum into a single scale, some informational detail is lost.

Applications: The metric has potential use in music information retrieval, speech analysis, and audio forensics for rapid comparison of timbral content or vibrato and formant movement. It is most useful as a complement to richer descriptors rather than a stand-alone feature.