A signal envelope is the smooth curve outlining the peaks of an oscillating signal — the instantaneous amplitude. In AM (amplitude modulation), the carrier frequency carries information in its envelope: x(t) = [1 + m·cos(2πf_m·t)]·cos(2πf_c·t). The envelope can be extracted via rectification + low-pass filtering, or analytically via the Hilbert transform: A(t) = |x(t) + i·H{x(t)}|. ADSR envelopes (Attack-Decay-Sustain-Release) shape the amplitude of synthesized sounds — the same math governs radar pulse shaping, speech recognition features, and neural spike detection.