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, fm is the maximum modulation frequency]] In radio communications, a sideband is a band of frequencies higher than or lower than the carrier frequency, that are the result of the modulation process. The sidebands carry the information transmitted by the radio signal. The sidebands comprise all the spectral components of the modulated signal except the carrier. The signal components above the carrier frequency constitute the upper sideband (USB), and those below the carrier frequency constitute the lower sideband (LSB). All forms of modulation produce sidebands.

Sideband creation

We can illustrate the creation of sidebands with one trigonometric identity: :$\cos\left(A\right)\cdot \cos\left(B\right) \equiv \tfrac\cos\left(A+B\right) + \tfrac\cos\left(A-B\right)$ Adding $\cos\left(A\right)$ to both sides: :$\cos\left(A\right)\cdot+\cos\left(B\right)= \tfrac\cos\left(A+B\right) + \cos\left(A\right) + \tfrac\cos\left(A-B\right)$ Substituting (for instance)  $A \triangleq 1000\cdot t$  and  $B \triangleq 100\cdot t,$  where $t$ represents time: :$\underbrace_\cdot \underbrace_ = \underbrace_ + \underbrace_ + \underbrace_.$ Adding more complexity and time-variation to the amplitude modulation also adds it to the sidebands, causing them to widen in bandwidth and change with time. In effect, the sidebands "carry" the information content of the signal.Tony Dorbuck (ed.), ''The Radio Amateur's Handbook, Fifty-Fifth Edition'', American Radio Relay League, 1977, p. 368

Sideband Characterization

In the example above, a cross-correlation of the modulated signal with a pure sinusoid, $\cos\left(\omega t\right),$ is zero at all values of $\omega$ except 1100, 1000, and 900. And the non-zero values reflect the relative strengths of the three components. A graph of that concept, called a Fourier transform (or ''spectrum''), is the customary way of visualizing sidebands and defining their parameters.

Amplitude modulation

Frequency modulation

Frequency modulation also generates sidebands, the bandwidth consumed depending on the modulation index - often requiring significantly more bandwidth than DSB. Bessel functions can be used to calculate the bandwidth requirements of FM transmissions.

Effects

Sidebands can interfere with adjacent channels. The part of the sideband that would overlap the neighboring channel must be suppressed by filters, before or after modulation (often both). In broadcast band frequency modulation (FM), subcarriers above 75kHz are limited to a small percentage of modulation and are prohibited above 99 kHz altogether to protect the ±75 kHz normal deviation and ±100 kHz channel boundaries. Amateur radio and public service FM transmitters generally utilize ±5 kHz deviation. To accurately reproduce the modulating waveform, the entire signal processing path of the system of transmitter, propagation path, and receiver must have enough bandwidth so that enough of the sidebands can be used to recreate the modulated signal to the desired degree of accuracy. In a non-linear system such as an amplifier, sidebands of the original signal frequency components may be generated due to distortion. This is generally minimized but may be intentionally done for the fuzzbox musical effect.