Radiansignal

Radiansignal is a term used in signal processing to denote a signal whose information content is primarily carried by its instantaneous phase, measured in radians, rather than by amplitude alone. In this framework, the signal is described by a phase function φ(t) ∈ R and, optionally, an amplitude envelope A(t); the common form is s(t) = A(t) cos(φ(t)).

If the amplitude is constant, the radiansignal becomes a pure phase-modulated carrier with information encoded in φ(t). In complex form, the baseband representation is s_c(t) = A(t) e^{j φ(t)}, and the real signal is the real part of that expression.

The instantaneous frequency is defined as ω(t) = dφ(t)/dt, in radians per second. Estimation of φ(t) often uses an analytic signal x_a(t) = x(t) + j H{x(t)} and φ(t) = atan2(Im{x_a(t)}, Re{x_a(t)}), followed by phase unwrapping to remove discontinuities.

Applications and variants: radiansignals arise in phase-modulation schemes such as PSK used in communications, in radar and sonar where phase carries information or is used for Doppler and range estimation, and in audio effects and synchronization tasks.

See also: Phase, Instantaneous frequency, Analytic signal, Complex baseband, Modulation.