THE ENVELOPE the magnitude of the phasor — amplitude kept, phase discarded
The envelope is the instantaneous amplitude of a signal — the smooth curve that rides its peaks. From a quadrature pair it is one step: |z| = √(I² + Q²). Taking the magnitude keeps the amplitude and throws the phase away — which is exactly what an AM detector, a power meter, or a spectrum display wants. It is the complement of the phase channel: where phase modulation puts everything in the angle, the envelope reads only the length. For the unit tone (I,Q)=(600,800) the envelope is a clean 1000 — a 3-4-5 triangle.
THE TECHNIQUE |z| = √(I² + Q²) — magnitude, dropping the phase
The demo takes the envelope of the quadrature pair (600,800) with an integer square root — exactly 1000, phase discarded: live demo
HISTORY & CREDIT envelope detection · |I + iQ|
“Magnitude and phase are equal partners in a sample.” — the envelope keeps only magnitude; the phase is deliberately dropped. cited
the magnitude · |z| = √(I² + Q²) — the length of the phasor. what is lost · the phase atan2(Q,I) — discarded; only amplitude remains. the uses · AM detection, power/RSSI meters, spectrum magnitude — when phase does not matter.
The length of the phasor kept and its angle let go — the amplitude channel, alone. magnitude only
RECOMMEND FOR I-13 the magnitude, on the compiler
On the canonical compiler, the envelope of (600,800) via integer square root is exactly 1000 — the 3-4-5 magnitude, phase gone:
Recommend as a NULL — the magnitude channel, and the phase’s complement. The envelope is the ordinary magnitude of the output; computing it (a square root, dart from batch 46) throws the phase away rather than carrying a new channel. It is the anti-phase-modulation: proof that magnitude is just the value while phase is the extra structure. NULL — and the clean foil that makes the phase-channel keeper shots legible.