amplitudevary

Amplitudevary is a descriptive term used in signal analysis to denote the degree to which the amplitude of a signal changes over time. It is not a universally standardized quantity, but a family of related measures that capture how strongly a signal's envelope fluctuates. In practice, amplitudevary is evaluated from the instantaneous amplitude of the signal's analytic form.

For a real-valued time signal x(t), form the analytic signal x_a(t) = x(t) + j H{x(t)}, where H denotes the Hilbert transform. The instantaneous amplitude (envelope) is A(t) = |x_a(t)|. A common summary of amplitude variation is the coefficient of variation of A(t) calculated over a chosen time window: CV_A = std(A(t)) / mean(A(t)). A simpler metric is the amplitude variation index (AVI) = (max(A) − min(A)) / mean(A). To capture time-varying behavior, a sliding window approach is often used: compute A(t) within successive windows and derive local statistics of A(t).

Interpretation of amplitudevary depends on context. High CV_A or AVI indicates substantial amplitude fluctuations, which may arise from modulation, transient events, or noise. Low values point to relatively stable amplitude. In practice, amplitudevary is used to assess dynamics in various domains, including audio processing (dynamic range and tremolo-like effects), communications (fading and modulation depth), and structural or seismic data where amplitude changes reflect underlying processes.

Limitations include sensitivity to noise and the choice of window length or scale. For nonstationary signals, multi-scale approaches may be employed to characterize amplitude variation across different time scales.