Uamplitude

Uamplitude is a theoretical quantity used in wave analysis to summarize the overall strength of a multi-component oscillatory signal. It extends the idea of a single-channel amplitude to signals composed of several orthogonal components by providing a single, dimensionless measure of their combined energy.

Calculation is typically described over a time window. If a signal has instantaneous amplitudes a1(t), a2(t), ..., an(t) for its components, the uamplitude UA can be defined as the square root of the time-averaged sum of the squares of the components: UA = sqrt( (1/T) ∫_0^T sum_i a_i(t)^2 dt ). In discrete form, UA = sqrt( (1/N) sum_t sum_i a_i(t)^2 ). In practice, UA is often normalized so that a reference signal yields UA = 1, allowing straightforward comparisons across signals.

Interpretation and uses: UA provides a compact representation of total signal strength that is less sensitive to how energy is distributed among frequencies or modes. It is useful for comparing signals with different spectral content, for quick quality assessments, and in simulations where a single scalar descriptor is convenient. However, it is not unique; the value depends on the chosen component set and the normalization, so it should be interpreted alongside component-wise analyses.

History and caveats: The concept originated in theoretical discussions of multi-mode wave fields and has appeared in academic literature and simulations as an aggregate metric. Users should be aware that UA depends on the basis and window used and may not capture details of individual components.