Amplitude modulation — the message rides the carrier's envelope, with sidebands in the spectrum.
Riding the Envelope
In AM, the carrier's amplitude follows the message signal:
s(t) = A_c [1 + m · m(t)] cos(2π f_c t)
- A_c is the unmodulated carrier amplitude
- m (modulation index, 0–1) controls how deeply the carrier is modulated
- m(t) is the message signal (normalized to [−1, 1])
- f_c is the carrier frequency
When m = 0, there's no modulation — just the carrier. At m = 0.5, the carrier envelope follows the message with 50% depth. At m = 1, the envelope touches zero at the message peaks — maximum depth without distortion. Overmodulation (m > 1) clips the carrier, producing distortion and additional sidebands.
The Spectrum
Despite being a time-varying amplitude, AM has a clean frequency-domain view: the carrier at f_c, and two sidebands at f_c ± f_m. The sideband amplitudes are m/2 relative to the carrier. Double-sideband suppressed-carrier (DSB-SC) and single-sideband (SSB) are variants that remove either the carrier or one sideband — more power-efficient but harder to demodulate.
The Frequency Shift Property
The multiplication of message and carrier in the time domain is a convolution in the frequency domain. The message's spectrum, centered at DC, gets shifted up to ±f_c — the carrier "lifts" the message to a radio frequency for transmission.
Experiment with the modulator: increase m to see the envelope deepen, change the message frequency to see the sidebands spread, and push m past 1 to see overmodulation clip the carrier. The dashed envelope curves show you exactly where the message traces the carrier amplitude.