Amplitudpowers

Amplitudpowers is a term used in signal analysis to describe a family of metrics that quantify the energy contained in the amplitude component of a modulated signal. The concept focuses on the envelope energy of a signal rather than the total energy that includes carrier and phase variations. It is often introduced in discussions of modulation dynamics and envelope sensing.

In a typical bandpass representation, a real-valued signal s(t) can be expressed in terms of an instantaneous amplitude A(t) and a carrier with phase or frequency variations, for example s(t) = A(t) cos(2π f_c t + φ(t)). The amplitudes are used to define amplitude power measures: the time-average amplitude power is P_A = lim T→∞ (1/T) ∫0^T [A(t)]^2 dt, and, for a stochastic amplitude process, P_A = E[A^2(t)]. When A(t) is extracted from s(t) via the analytic signal s_a(t) = s(t) + i H{s(t)} (where H denotes the Hilbert transform), A(t) = |s_a(t)|.

These measures help characterize how energy is distributed in the amplitude domain, independent of high-frequency carrier components. Applications appear in communications to study modulation depth and envelope dynamics, in audio processing to inform dynamic range control, and in radar and sensing where envelope information is critical. Limitations include dependence on the method used to extract A(t) and potential ambiguities for signals with intertwined amplitude and phase components.

See also: Amplitude modulation, Envelope detector, Hilbert transform, Instantaneous power, Signal power.