Sidebands

Sidebands are components in the frequency spectrum of a modulated signal that appear symmetrically around a carrier frequency. They arise when a carrier is modulated by another signal, the information signal. The carrier frequency f_c is accompanied by sidebands at f_c ± f_m, where f_m is a frequency component of the modulating signal. The upper sideband is f_c + f_m, and the lower sideband is f_c − f_m.

In amplitude modulation, a carrier is modulated as s(t) = [A_c + m(t)] cos(2π f_c t). If m(t) contains frequency components at f_m, sidebands appear at f_c ± f_m. If m(t) is a pure tone, two discrete sidebands appear around f_c with equal amplitude. The carrier and sidebands together form the modulated spectrum.

Types and usage: Double-sideband with carrier (standard AM) includes both sidebands and the carrier. Double-sideband suppressed-carrier (DSB-SC) removes the carrier to save power. Single-sideband (SSB) suppresses one sideband (either USB or LSB), greatly reducing bandwidth and is widely used in radio communications.

In frequency modulation (FM) and phase modulation (PM), the modulating signal produces an extended set of sidebands with amplitudes described by Bessel functions. The overall bandwidth can be estimated by Carson’s rule: B ≈ 2(Δf + f_mmax), where Δf is the peak frequency deviation. Sidebands thus play a central role in determining the information-carrying capacity and bandwidth requirements of modulated systems.

Applications and analysis: Sidebands are observed with spectrum analyzers, and demodulation schemes extract the original information from the carrier and its sidebands.