Phasorina

Phasorina is a conceptual representation used in signal processing to capture the phase and amplitude information of periodic signals in a compact form. The term is built from “phasor” and the suffix -ina to denote a derived, simplified version of the traditional phasor description.

Formally, for a real-valued periodic signal x(t) with fundamental frequency ω0 and harmonic components, the phasorina approach assigns to each harmonic n a complex phasor p_n = A_n e^{jφ_n}, where A_n is the harmonic amplitude and φ_n its phase. The phasorina vector P is the collection {p_n} across relevant harmonics. The original signal can be reconstructed, approximately, by summing the harmonically weighted phasors, x(t) ≈ A0 + sum_{n≥1} Re{p_n e^{j n ω0 t}}.

Operations on phasorinas mirror standard linear signal processing: time shifts multiply each phasor by a phase factor, and linear combinations of signals translate into linear combinations of their phasorinas. This representation emphasizes inter-harmonic phase relationships and tends to simplify certain analyses, especially those focused on coherence and synchronization among harmonics. It also offers a compact data format for implementations in digital signal processing where multiple harmonics are managed together.

Applications include visualization of phase relationships in complex waveforms, teaching Fourier-style concepts, and lightweight analysis in power systems and communications. The phasorina framework is presented as an accessible alternative or complement to the Fourier transform and the analytic signal, particularly for tasks centered on phase alignment and harmonic interaction. See also: phasor, Fourier series, analytic signal.