amplitudow

Amplitudow is a hypothetical quantity used in the study of wave dynamics and signal analysis. It serves as a dimensionless measure of the instantaneous amplitude of a waveform relative to a chosen reference level, allowing comparison of amplitude dynamics across different systems or conditions.

In practice, amplitudow is defined from a real-valued signal s(t) by first forming the analytic signal z(t) = s(t) + i H{s(t)}, where H denotes the Hilbert transform. The envelope is E(t) = |z(t)|. With a reference amplitude A_ref selected for the system, amplitudow(t) is given by amplitudow(t) = E(t) / A_ref. This yields a time-varying, unitless quantity that reflects how the instantaneous amplitude tracks the reference.

Origin and naming of the term are fictional, stemming from a hypothetical field often described in illustrative literature as wavecraft. The concept is used to compare amplitude modulation and envelope behavior across devices and environments without committing to a specific physical frequency or carrier.

Properties and interpretation: amplitudow is non-negative and typically bounded by the chosen reference, though practical constraints and data processing steps can affect bounds. It emphasizes relative amplitude changes rather than absolute signal strength, making it useful for cross-system comparisons, quality assessment, and modulation analysis. It is distinct from raw amplitude, RMS amplitude, or instantaneous phase, and is most meaningful when a consistent reference A_ref is applied.

Limitations: as a constructed measure, amplitudow depends on the reference choice and on the method used to compute the envelope. It should be used alongside standard metrics to avoid misinterpretation.

See also: amplitude envelope, Hilbert transform, amplitude modulation, signal normalization.