D09-F06-A03 · LEVEL 2 GUIDED LAB · SYNTHETIC DATA

Hilbert Transform Phasor Components

What in-phase and quadrature components describe the local analytic signal? Walk the evidence clock one stage at a time. This lab teaches the publication contract; it does not simulate returns, platform parity, or trade performance.

Selected expression

analytic approximation z_t=I_t+jQ_t; amplitude=sqrt(I_t^2+Q_t^2); phase=atan2(Q_t,I_t)

Availability rule

An output at t may use only finite, basis-consistent observations available through t; chart alignment never moves the information clock backward.

calculated · step 1 of 7

Verified synthetic fixture

This lab is paired with datasets/implementation-fixtures.json: 96 deterministic, oldest-to-newest observations spanning oscillating, rising, and moderating regimes. It is teaching data—not market history or predictive evidence.

Canonical latest output (D09-F06-A03)
{
  "in_phase": -0.8607335347476948,
  "quadrature": 0.16777396655856047,
  "amplitude": 0.8769323358697945,
  "phase": 2.9490866862859964
}

Executable checks cover this result, flat/zero-volume boundaries, invalid timestamps, and prefix causality in both language entry points.