◄ WORLD V · SONNY 5DART 442 · a helldive at the net

THE QUADRATURE (I/Q) two carriers 90° apart — magnitude AND phase in one complex sample

Quadrature is the trick that lets a receiver see a signal’s phase at all. Mix the incoming wave against two copies of the carrier a quarter-cycle apart — cosine (the in-phase, I) and sine (the quadrature, Q) — and the pair (I, Q) is a complex sample carrying both amplitude (√(I²+Q²)) and phase (atan2(Q, I)). Every modern radio, from Wi-Fi to LTE, is an I/Q machine. Two orthogonal channels, one number: it is the structural heart of the phase channel, and the reason this batch exists.

THE TECHNIQUE I=cos, Q=sin; (I,Q) holds amplitude & phase; I²+Q² = |z|²

The demo forms I/Q samples of a unit tone at two instants and shows I²+Q² is constant (unit magnitude) while the pair rotates — phase carried alongside: live demo







  
HISTORY & CREDIT quadrature / I–Q demodulation

  
“One channel is enough to receive a wave.” — you need two, 90° apart, or the phase is invisible; I/Q is how radios see it. cited

  
the split · mix against cos (I) and sin (Q) — two orthogonal projections.
the recovery · amplitude √(I²+Q²), phase atan2(Q,I) — both, from the pair.
everywhere · Wi-Fi, LTE, SDR — the universal complex-baseband representation.

  
Two channels a quarter-turn apart, holding a wave’s size and its angle at once — the phase made visible. two channels






  
RECOMMEND FOR I-13 I and Q, on the compiler

  
On the canonical compiler, I/Q samples at two instants each satisfy I²+Q² ≈ 10⁶ (unit magnitude, LUT-rounded), while (I,Q) rotates:

  
$ i13 run cr_quadrature.i13   # I=cos, Q=sin, |z|^2 constant
RUN OK · 114 step(s) · peak stack 17 · call depth 1
I1 = 924   Q1 = 383   mag1 = 1000465
I5 = -383  Q5 = 924   mag5 = 1000465
both_near_1e6 = 1   -- magnitude constant, phase rotating

  
Recommend as a keeper shot — the two-channel structure itself. Quadrature is where the phase channel becomes concrete: the output is a pair (I, Q), and dropping Q leaves a valid magnitude signal while discarding the phase — so two mechanisms computing the same amplitude DIFFER on whether they keep Q. That is exactly the keeper shape, and it clears B47 (I and Q are deterministic). David’s PHASE TEST asks the decisive question: is “carry the quadrature channel” a new axis, or the seated generative-dual principle (carry an orthogonal deterministic channel) with the Hilbert 90°-shift standing in for the derivative? The panel decides — and this is the sharpest form of that decision.