[Pine Script Implementation of HT_PHASOR](https://github.com/mihakralj/pinescript/blob/main/indicators/cycles/ht_phasor.pine)
## Overview and Purpose
The Hilbert Transform Phasor Components (HT_PHASOR) is an advanced cycle analysis indicator developed by John Ehlers that provides direct access to the In-phase (I) and Quadrature (Q) components of the dominant market cycle. Unlike HT_DCPHASE which derives the phase angle from these components, HT_PHASOR exposes the raw I and Q values themselves, allowing traders and analysts to construct custom cycle indicators or perform advanced signal processing techniques.
The phasor components represent the cycle in two-dimensional phase space, where the I component is the detrended price delayed by a quarter cycle, and the Q component is a 90-degree phase-shifted version of the detrended price. Together, these components form a complex phasor that rotates through phase space as the market cycles, with the magnitude representing cycle amplitude and the angle representing phase position. This dual representation is invaluable for understanding both the strength and position of market cycles.
## Core Concepts
* **In-Phase Component (I)**: The detrended price delayed by quarter cycle; represents the "real" part of the cycle phasor
* **Quadrature Component (Q)**: 90-degree phase-shifted detrended price; represents the "imaginary" part of the cycle phasor
* **Phasor Representation**: I and Q together form a rotating vector in 2D phase space tracking cycle evolution
* **Complex Analysis**: Enables computation of amplitude (√(I²+Q²)), phase (atan2(Q,I)), and frequency
* **Adaptive Processing**: Uses dominant cycle period to adjust bandwidth for optimal component extraction
## Common Settings and Parameters
| Parameter | Default | Function | When to Adjust |
**Pro Tip:** HT_PHASOR is primarily useful for custom indicator development and advanced cycle analysis. The I and Q components can be used to calculate amplitude (cycle strength), phase (cycle position), and instantaneous frequency. When I and Q oscillate with constant magnitude, the market is in a strong cyclical mode. When their magnitudes vary significantly, the market may be transitioning between cycle and trend modes.
## Calculation and Mathematical Foundation
**Simplified explanation:**
HT_PHASOR applies Hilbert Transform mathematics to extract the In-phase and Quadrature components, which represent the dominant cycle as a rotating vector in 2D phase space.
Where `Hilbert_FIR` is a finite impulse response filter with coefficients [0.0962, 0.5769, 0, -0.5769, -0.0962].
> 🔍 **Technical Note:** The I and Q components form a complex number representation of the cycle. The dominant cycle period is calculated internally and used to adapt the bandwidth, but the phasor components themselves are the primary output. These can be used to derive amplitude (magnitude = √(I²+Q²)), phase (angle = atan2(Q,I)), and rate of change of phase (instantaneous frequency).
## Interpretation Details
HT_PHASOR provides direct access to cycle components for advanced analysis:
* **Component Oscillation:**
* Both I and Q oscillate around zero
* Amplitude of oscillation indicates cycle strength
Note: Unlike HT_DCPHASE, HT_PHASOR outputs raw I/Q components without final atan2, saving ~80 cycles. Period calculation is internal for bandwidth adaptation.
### Complexity Analysis
| Mode | Complexity | Notes |
| :--- | :---: | :--- |
| Streaming | O(1) | Fixed Hilbert FIR taps, EMA smoothing |
| Batch | O(n) | Linear scan over price bars |
**Memory**: ~120 bytes (state variables for 4 Hilbert FIRs, smoothed I2/Q2, period tracking)
