THE AMPLITUDE MODULATION — a dart

AMPLITUDE MODULATION the message rides the envelope — the oldest way to send a voice

Amplitude modulation is the first modulation ever broadcast: multiply a steady high-frequency carrier by (1 + m·x(t)), and the message x(t) becomes the envelope — the slow rise and fall traced by the carrier’s peaks. A crystal set recovers it with nothing but a diode and a capacitor: rectify, smooth, and the envelope reappears. It is simple and robust, and it is the counterpoint to phase modulation — here everything is in the magnitude, and the phase is idle. AM radio has carried voices since 1906.

THE TECHNIQUE s = (C + msg)·carrier; the peak amplitude carries the message

The demo builds an AM sample at the carrier peak and reads the envelope back off it — the message is the peak amplitude: live demo

HISTORY & CREDIT Fessenden 1906 · AM broadcasting

“Radio needs complex circuitry to decode.” — an AM envelope comes off with a diode and a capacitor; the message is just the peak height. cited

the modulation · s(t) = (C + m·x(t))·cos(ωt) — the message scales the carrier’s height.
the envelope · rectify + smooth → C + m·x(t) reappears — envelope detection.
1906 · Reginald Fessenden — the first AM voice broadcast.

A voice written into the height of a wave — the phase idle, the magnitude everything. amplitude channel

RECOMMEND FOR I-13 the envelope, on the compiler

On the canonical compiler, an AM sample at the carrier peak (LUT=1000) with envelope C+msg=8 reads back exactly 8:

$ i13 run cr_amplitudemodulation.i13 # s = (C+msg)*carrier RUN OK · 56 step(s) · peak stack 17 · call depth 0 C = 5 msg = 3 peak_sample = 8000 -- (5+3) * SINE[peak=1000] envelope = 8 recovered = 1 -- the message is the peak amplitude

Recommend as a NULL — and the phase channel’s foil. AM puts the message in the magnitude, which is the ordinary output value; recovering it is envelope detection, a plain read of the amplitude. There is no extra orthogonal channel here — the message IS the output — so nothing to seat. It earns its place as the deliberate contrast to dart 438: same carrier, opposite channel. Where PM tests the phase, AM confirms the magnitude is just the value. NULL.