amplitudimoduloidun

Amplitudimoduloidun is a hypothetical operation in signal processing that consists of applying a modulus to the instantaneous amplitude of a signal, producing a wrap-around of amplitude values within a fixed range while leaving the carrier’s phase reference largely unaltered. The concept is primarily used as a thought experiment or a compact way to study nonlinearly constrained envelopes and their spectral consequences.

Mathematically, let a signal be s(t) with instantaneous amplitude A(t) and phase φ(t), so s(t) ≈ A(t) cos(φ(t)) for a narrowband carrier. The amplitudimoduloidun transform defines A′(t) = M(A(t)) where M(a) = a − ⌊a/L⌋·L and L > 0 is the chosen modulus. The transformed signal is then written as s′(t) = A′(t) cos(φ(t)). In practice, the phase reference may be preserved in the sense that φ(t) is not directly altered by the modulus operation, but the nonlinearity in A′(t) changes the overall waveform and its spectrum.

Key properties include its deterministic, nonlinear nature and its tendency to introduce harmonic content even when the original signal is spectrally simple. The operation maintains amplitude within a fixed interval [0, L) (or a chosen symmetric range with a signed variant) and can cause abrupt changes in A′(t) when A(t) crosses modulus boundaries, producing characteristic sawtooth-like envelopes.

Variants of the idea allow a time-varying modulus L(t) or a complex-baseband formulation, broadening the range of theoretical analyses and computer simulations. Amplitudimoduloidun is discussed primarily in academic contexts as a model of amplitude wrap-around and as a contrast to clipping and saturation effects in nonlinear systems. See also amplitude modulation, modulus operation, nonlinear distortion.