QuanTAlib/lib/cycles/ht_phasor/HtPhasor.md

HT_PHASOR: Hilbert Transform - Phasor Components

"Phasors let us measure a cycle's position and strength; trading becomes geometry over time."

HT_PHASOR decomposes the price signal into two orthogonal components: InPhase (I) and Quadrature (Q) using the Hilbert Transform. These components form a complex phasor (Z = I + jQ) that describes the instantaneous amplitude and phase of the market cycle.

Historical Context

John Ehlers introduced the decomposition of market data into phasor components in Rocket Science for Traders (2001). This decomposition is fundamental to his entire suite of cycle indicators (SineWave, Homodyne, etc.).

TA-Lib implements HT_PHASOR to expose these intermediate components directly for advanced analysis. QuanTAlib matches the TA-Lib implementation.

Architecture & Physics

The calculation pipeline extracts the analytic signal's real and imaginary components.

1. WMA Smoothing

SmoothPrice_t = \frac{4P_t + 3P_{t-1} + 2P_{t-2} + P_{t-3}}{10}

2. Hilbert Transform

Applied to smoothed price with adaptive bandwidth to generate fundamental components.

3. Phasor Components

I2_t = I1_t - jQ_t

Q2_t = Q1_t + jI_t

Where:

• InPhase (I): Smoothed I2—cycle signal aligned with price
• Quadrature (Q): Smoothed Q2—rate of change (velocity) of cycle

Note: InPhase output is delayed by 3 bars to align with Quadrature's effective lag.

4. Phase Relationship

• Q leads I by 90°
• When I peaks, Q crosses zero (downward)
• When I crosses zero (upward), Q peaks

Performance Profile

Operation Count (Streaming Mode, per Bar)

Operation	Count	Cost (cycles)	Subtotal
MUL (Hilbert taps)	28	3	84
MUL (phasor calc)	8	3	24
ADD/SUB	35	1	35
EMA smoothing	4	4	16
Total	75	—	~159 cycles

Complexity Analysis

• Streaming: O(1) per bar—fixed Hilbert cascade
• Memory: ~1.2 KB per instance (circular buffers)
• Warmup: 32 bars (TA-Lib lookback)

Validation

Library	Status	Notes
TA-Lib	✅	Matches TALib.Functions.HtPhasor()
Skender	N/A	Not implemented
PineScript	✅	Matches phasor.pine

Usage & Pitfalls

• Dual output—InPhase (Value) and Quadrature (property)
• 32-bar warmup required—ignore early values
• Capture Quadrature immediately after Update()—property updated on each call
• Trending markets break orthogonality—use HT_TRENDMODE to filter
• Phasor crossover:
  • Buy: Q crosses I from below (anticipates cycle trough)
  • Sell: Q crosses I from above (anticipates cycle peak)
• For sine input sin(ωt): InPhase ≈ sin(ωt), Quadrature ≈ cos(ωt)

API

classDiagram
    class HtPhasor {
        +double Value
        +double Quadrature
        +bool IsHot
        +HtPhasor()
        +HtPhasor(ITValuePublisher source)
        +TValue Update(TValue input, bool isNew)
        +void Reset()
    }

Class: HtPhasor

Parameter	Type	Default	Range	Description
(none)	—	—	—	No constructor parameters

Properties

• Value (double): InPhase component of phasor
• Quadrature (double): Quadrature component (90° shifted)
• IsHot (bool): Returns true when warmup (32 bars) is complete

Methods

• Update(TValue input, bool isNew): Updates the indicator with a new data point

C# Example

using QuanTAlib;

// Create HT_PHASOR
var htPhasor = new HtPhasor();
double prevInPhase = 0, prevQuadrature = 0;

// Update with streaming data
foreach (var bar in quotes)
{
    var result = htPhasor.Update(new TValue(bar.Date, bar.Close));
    double inPhase = result.Value;
    double quadrature = htPhasor.Quadrature;  // Capture immediately!
    
    if (htPhasor.IsHot)
    {
        Console.WriteLine($"{bar.Date}: I = {inPhase:F4}, Q = {quadrature:F4}");
        
        // Phasor crossover detection
        if (inPhase > quadrature && prevInPhase <= prevQuadrature)
            Console.WriteLine("  → Bullish crossover (anticipate trough)");
        else if (inPhase < quadrature && prevInPhase >= prevQuadrature)
            Console.WriteLine("  → Bearish crossover (anticipate peak)");
    }
    
    prevInPhase = inPhase;
    prevQuadrature = quadrature;
}

// Batch calculation
var output = HtPhasor.Calculate(sourceSeries);