Psignal

Psignal is a conceptual framework in signal processing describing a family of signals whose amplitude and phase can be controlled separately through a parameterized model. The term is used to denote representations where the instantaneous value is expressed as s(t) = A(t) cos(φ(t)), with A(t) as a real-valued envelope and φ(t) as a phase function. This separation enables flexible waveform design, modulation, and analysis, particularly when precise shaping of both amplitude and phase is required.

In practice, Psignal supports tasks such as adaptive modulation, where A(t) and φ(t) are updated in real time, and synthesis, where complex waveforms are generated from low-dimensional controls. It is related to, but distinct from, traditional amplitude modulation, phase modulation, and IQ representations, since Psignal emphasizes the explicit independence of the two components as a design knob.

Applications include communications systems, audio synthesis, radar and sonar waveform design, and control systems where phase tracking matters. Advantages cited for Psignal representations include intuitive control of waveform shape, robust reconstruction from partial observations, and compatibility with parametric optimization methods. Challenges include choosing stable parameterizations for A(t) and φ(t), avoiding aliasing in discrete implementations, and ensuring perceptual or system constraints are met. Research areas include learning-based parameterizations, efficient real-time algorithms, and integration with existing DSP pipelines.

See also: amplitude modulation, phase modulation, analytic signal, quadrature signaling, waveform synthesis.