Editing Sideband

{{Short description|Radio communications concept}}
{{about|radio communications|participation in other music projects|Side project}}

[[Image:Am-sidebands-en.svg|thumb|300px|right|The power of an AM radio signal plotted against frequency. '''fc''' is the [[carrier frequency]], '''fm''' is the maximum modulation frequency]]

In [[radio]] communications, a '''sideband''' is a [[band (radio)|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 component]]s 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''':'''

:<math>\cos(A)\cdot \cos(B) \equiv \tfrac{1}{2}\cos(A+B) + \tfrac{1}{2}\cos(A-B)</math>

Adding <math>\cos(A)</math> to both sides''':'''

:<math>\cos(A)\cdot [1+\cos(B)] = \tfrac{1}{2}\cos(A+B) + \cos(A) + \tfrac{1}{2}\cos(A-B)</math>

Substituting (for instance) &nbsp;<math>A \triangleq 1000\cdot t</math>&nbsp; and &nbsp;<math>B \triangleq 100\cdot t,</math>&nbsp; where <math>t</math> represents time''':'''

:<math>\underbrace{\cos(1000\ t)}_{\text{carrier wave}}\cdot \underbrace{[1+\cos(100\ t)]}_{\text{amplitude modulation}}
= \underbrace{\tfrac{1}{2}\cos(1100\ t)}_{\text{upper sideband}}
+ \underbrace{\cos(1000\ t)}_{\text{carrier wave}}
+ \underbrace{\tfrac{1}{2}\cos(900\ t)}_{\text{lower sideband}}.</math>

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.<ref>Tony Dorbuck (ed.), ''The Radio Amateur's Handbook, Fifty-Fifth Edition'', American Radio Relay League, 1977, p. 368</ref>

===Sideband Characterization===

In the example above, a [[cross-correlation]] of the modulated signal with a pure sinusoid, <math>\cos(\omega t),</math> is zero at all values of <math>\omega</math> 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.

[[File:Modulated radio signal frequency spectrum.svg|thumb|upright=1.4|[[Frequency]] spectrum of a typical modulated AM or FM radio signal.]]

==Amplitude modulation==

[[Amplitude modulation]] of a [[carrier signal]] normally results in two mirror-image sidebands. The signal components above the carrier frequency constitute the upper sideband (USB), and those below the carrier frequency constitute the lower sideband (LSB). For example, if a 900{{nbsp}}kHz carrier is amplitude modulated by a 1{{nbsp}}kHz audio signal, there will be components at 899{{nbsp}}kHz and 901{{nbsp}}kHz as well as 900{{nbsp}}kHz in the generated [[radio frequency]] spectrum; so an [[Audio signal|audio]] [[Bandwidth (signal processing)|bandwidth]] of (say) 7{{nbsp}}kHz will require a [[radio spectrum]] bandwidth of 14{{nbsp}}kHz. In conventional AM [[transmission (telecommunications)|transmission]], as used by ''broadcast band'' AM stations, the original audio signal can be recovered ("detected") by either [[synchronous detector]] circuits or by simple [[envelope detector]]s because the carrier and both sidebands are present. This is sometimes called '''double sideband amplitude modulation''' ('''DSB-AM'''), but not all variants of DSB are compatible with envelope detectors.

In some forms of AM, the carrier may be reduced, to save power. The term [[double-sideband reduced-carrier transmission|''DSB reduced-carrier'']] normally implies enough carrier remains in the transmission to enable a [[Receiver (radio)|receiver]] circuit to regenerate a strong carrier or at least [[synchronous|synchronise]] a [[phase-locked loop]] but there are forms where the carrier is removed completely, producing [[double-sideband suppressed-carrier transmission|double sideband with ''suppressed'' carrier]] (DSB-SC). Suppressed carrier systems require more sophisticated circuits in the receiver and some other method of deducing the original carrier frequency. An example is the [[stereophonic]] difference (L-R) information transmitted in stereo [[FM broadcasting]] on a 38&nbsp;kHz [[subcarrier]] where a low-power signal at half the 38-kHz carrier frequency is inserted between the monaural signal frequencies (up to 15{{nbsp}}kHz) and the bottom of the stereo information sub-carrier (down to 38–15{{nbsp}}kHz, i.e. 23{{nbsp}}kHz). The receiver locally regenerates the subcarrier by doubling a special 19&nbsp;kHz [[Pilot signal|pilot tone]]. In another example, the [[Quadrature amplitude modulation|quadrature modulation]] used historically for chroma information in [[PAL]] television broadcasts, the synchronising signal is a short burst of a few cycles of carrier during the [[analog television#Structure of a video signal|"back porch"]] part of each scan line when no image is transmitted.  But in other DSB-SC systems, the carrier may be regenerated directly from the sidebands by a [[Costas loop]] or [[squaring loop]]. This is common in digital transmission systems such as [[BPSK]] where the signal is continually present.

[[Image:AM signal.jpg|thumb|200px|right|Sidebands are evident in this [[spectrogram]] of an AM broadcast (The carrier is highlighted in red, the two mirrored audio spectra (green) are the lower and upper sideband). Time is represented along the vertical axis; the magnitude and frequency of the side bands changes with the program content.]]
If part of one sideband and all of the other remain, it is called [[vestigial sideband]], used mostly with [[television]] [[broadcasting]], which would otherwise take up an unacceptable amount of [[Bandwidth (signal processing)|bandwidth]].  Transmission in which only one sideband is transmitted is called [[single-sideband modulation]] or SSB.  SSB is the predominant voice mode on [[Shortwave|shortwave radio]] other than [[shortwave#Shortwave broadcasting|shortwave broadcasting]]. Since the sidebands are mirror images, which sideband is used is a matter of convention.

In SSB, the [[suppressed carrier|carrier is suppressed]], significantly reducing the [[electric power|electrical power]] (by up to 12{{nbsp}}dB) without affecting the information in the sideband. This makes for more efficient use of transmitter power and RF bandwidth, but a [[beat frequency oscillator]] must be used at the [[receiver (radio)|receiver]] to reconstitute the carrier. If the reconstituted carrier frequency is wrong then the output of the receiver will have the wrong frequencies, but for speech small frequency errors are no problem for intelligibility. Another way to look at an SSB receiver is as an RF-to-audio frequency [[transposition (music)|transposer]]: in USB mode, the dial frequency is subtracted from each radio frequency component to produce a corresponding audio component, while in LSB mode each incoming radio frequency component is subtracted from the dial frequency.

==Frequency modulation==
[[Frequency modulation]] also generates sidebands, the bandwidth consumed depending on the [[Frequency modulation|modulation index]] - often requiring significantly more bandwidth than DSB. [[frequency modulation#Bessel functions|Bessel functions]] can be used to calculate the bandwidth requirements of FM transmissions. [[Carson's rule]] is a useful approximation of bandwidth in several applications.

==Effects==

Sidebands can [[interference (communication)|interfere]] with [[adjacent channel]]s. The part of the sideband that would overlap the neighboring channel must be suppressed by [[filter (signal processing)|filter]]s, before or after modulation (often both).  In [[broadcast band]] [[frequency modulation]] (FM), [[subcarrier]]s above 75{{nbsp}}[[kHz]] are limited to a small [[percent]]age of modulation and are prohibited above 99&nbsp;kHz altogether to protect the ±75&nbsp;kHz normal [[Frequency deviation|deviation]] and ±100&nbsp;kHz [[Frequency channel|channel]] boundaries. [[Amateur radio]] and public service FM transmitters generally utilize ±5&nbsp;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.

==See also==
* [[Independent sideband]]
* [[Out-of-band data|Out-of-band]] communications involve a channel other than the main communication channel.
* [[Side lobe]]
* [[Sideband computing]] is a distributed computing method using a channel separate from the main communication channel.
* [[TV transmitter]]

==References==
{{reflist}}
{{refbegin}}
* {{FS1037C MS188}}
* [[United States Department of the Army|Department of The Army]] Technical Manual TM 11-685 "Fundamentals of Single Sideband Communications"
{{refend}}

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[[Category:Amateur radio]]