HT_PHASOR decomposes the price signal into two orthogonal components, InPhase ($I$) and Quadrature ($Q$), using the Hilbert Transform. Together these form a complex phasor $Z = I + jQ$ that describes the instantaneous amplitude and phase of the dominant market cycle. Compatible with TA-Lib's `HT_PHASOR` function, this dual-output indicator provides the fundamental building blocks for cycle analysis, phasor crossover timing, and instantaneous amplitude measurement.
John Ehlers introduced phasor decomposition of market data in *Rocket Science for Traders* (2001). In electrical engineering, a phasor represents a sinusoidal signal as a rotating complex vector, separating the cycle's "position" (InPhase) from its "velocity" (Quadrature). Ehlers recognized that this decomposition is the mathematical foundation for all his cycle indicators: HT_SINE, HT_DCPERIOD, HT_DCPHASE, and HOMOD all derive from these same I/Q components. TA-Lib exposes HT_PHASOR to give advanced users direct access to the analytic signal for custom cycle analysis. The InPhase output is delayed by 3 bars to align with the Quadrature component's effective lag from the Hilbert Transform FIR.
Using Ehlers' coefficients ($A = 0.0962$, $B = 0.5769$), the 4-tap discrete Hilbert approximation generates the detrender, and from it the fundamental In-Phase and Quadrature components ($I_1$, $Q_1$). Further Hilbert transforms of these produce $jI$ and $jQ$.
$Q$ leads $I$ by $90°$. When $I$ peaks, $Q$ crosses zero downward. When $I$ crosses zero upward, $Q$ peaks. The instantaneous amplitude is $A = \sqrt{I^2 + Q^2}$ and the instantaneous phase is $\phi = \arctan(Q/I)$.
