timefrequencywetness

Timefrequencywetness is a scalar measure used in signal processing to describe how the energy of a signal is distributed across time and frequency in its time-frequency representation. It quantifies the degree to which a signal’s energy is spread out (wet) over the time-frequency plane versus concentrated in localized regions (dry). The concept is closely related to notions of time-frequency concentration and sparsity, and can be employed to compare signals or processing methods in terms of how they alter the energy distribution.

A common formulation relies on a time-frequency representation such as the short-time Fourier transform or a wavelet transform. Let E(t,f) be the nonnegative energy distribution, for example E(t,f) = |X(t,f)|^2, and normalize it so that the sum over all time and frequency bins equals one. The timefrequencywetness W is then defined as a normalized entropy of E: H = - sum E(t,f) log E(t,f), and W = H / log(K), where K is the number of time-frequency bins. Higher W indicates greater diffusion of energy across the time-frequency plane, while lower W indicates energy concentrated in fewer bins. Alternative definitions use other entropy measures (e.g., Rényi entropy) or sparsity-based indices.

Applications include characterizing transient versus sustained content in audio, evaluating time-frequency representations, and feature extraction for machine learning. Limitations include dependence on the chosen time-frequency representation and resolution, sensitivity to noise, and interpretation that can vary with binning and normalization.