# Signal modulation **Signal modulation** is the systematic variation of one or more properties of a periodic [[Carrier_wave|carrier wave]] — its amplitude, its frequency, or its phase — in step with a separate message signal, so that the message can travel across a [[Communication_channel|communication channel]], share a physical medium with other messages, or survive storage and later retrieval. A carrier by itself carries no information; impressing a message onto it is exactly what the *Modulation* microsim on this page shows, letting the reader switch one message between seven modulation schemes and watch the same information reshape a completely different-looking wave and its spectrum. Two practical reasons make modulation almost universal in electronic communication. A message such as a voice signal occupies a low range of frequencies, and radiating it efficiently and directly as an electromagnetic wave would need an antenna a sizeable fraction of a wavelength long — kilometers, for an audio-frequency wave. Shifting the message up onto a much higher carrier frequency shrinks the antenna to a workable size. The second reason is sharing: once a message rides on a carrier, many messages can occupy the same wire, optical fiber, or stretch of air at once, each on its own carrier frequency, a scheme that [[Telecommunications|telecommunications]] and broadcast systems both depend on. The families below divide by how the carrier's state is chosen. Analog methods vary amplitude, frequency, or phase continuously. Digital methods choose among a finite set of carrier states once per symbol interval, trading raw bandwidth for resistance to noise. Pulse methods carry the message either as a train of varying analog pulses or as a fully digital, quantized bitstream. A further group of techniques spreads a signal's energy across a wide band, or across several antennas, for reasons the first three families do not address. ## Analog modulation methods A sinusoidal carrier has exactly three properties available to vary: its amplitude, its instantaneous frequency, and its phase, since any sinusoid can be written as the real part of a rotating phasor whose length, spin rate, and starting angle are those three quantities.[^john021] [[Amplitude_modulation]] varies the first: in the sketch, `s(t) = [1 + β·m(t)]·cos(2π f_c t)` multiplies the carrier's amplitude by one plus the (scaled) message, so the envelope traces the message shape directly. The other two properties belong to angle modulation. [[Frequency_modulation]] varies the carrier's instantaneous frequency in proportion to the message; phase modulation varies the phase angle directly. Because instantaneous frequency is the rate of change of phase, the two are formally the same operation applied to different functions of the message: the sketch computes frequency modulation as `s(t) = cos(2π f_c t + β·∫m(t)dt)` and phase modulation as `s(t) = cos(2π f_c t + β·m(t))`, so a phase modulator fed the running integral of a message produces the same wave as a frequency modulator fed the message itself. Single-sideband and vestigial-sideband modulation are amplitude-modulation variants that filter away part of the redundant spectrum an ordinary amplitude-modulated signal carries, trading circuit complexity for bandwidth and transmitted power. ## Digital modulation methods Digital modulation restricts the carrier to a finite alphabet of states, chosen once per symbol interval, rather than letting a property vary continuously. The three carrier properties still supply the alphabet: on-off or multilevel keying of amplitude gives [[Amplitude-shift_keying|amplitude-shift keying]], switching among a small set of frequencies gives [[Frequency-shift_keying|frequency-shift keying]], and switching among phase angles gives [[Phase-shift_keying|phase-shift keying]]. A modulator that can choose among *M* distinguishable states packs log2 *M* bits into every symbol, so a scheme with more states moves more bits per symbol at the same signalling rate, at the cost of demanding a larger signal-to-noise ratio to keep the same error rate; on a [[Constellation_diagram|constellation diagram]] this shows up as points packed closer together and therefore easier for noise to confuse.[^ell134] Detection falls into two families. A coherent detector tracks the carrier's phase and compares the received symbol against a reference, which is more sensitive but requires a receiver that can recover that phase; a noncoherent detector only measures energy or frequency and needs no phase reference, at a cost in performance. On-off keying, the simplest amplitude scheme, needs about twice the energy per bit that binary phase-shift keying needs for the same bit-error rate, and detecting it noncoherently costs roughly another decibel beyond that.[^ell149] The common techniques in use — on-off keying, binary and quadrature phase-shift keying, higher-order phase and quadrature-amplitude schemes, and multilevel frequency-shift keying — trade the same currency: denser constellations need more energy per bit, while spreading symbols across more frequencies, as in multilevel frequency-shift keying, can actually reduce the energy a receiver needs as the number of tones grows.[^ell158] A receiver that does not know which scheme it is listening to can often still identify it from statistics of the received waveform alone, a task called automatic digital modulation recognition, useful in spectrum monitoring and software-defined radios that must adapt to an unknown transmitter. Digital information can also be impressed on a channel with no carrier at all, as a baseband train of pulses whose levels or transitions stand for symbols directly; this baseband case shares its symbol-and-noise mathematics with carrier-based keying even though no carrier frequency is involved. ## Pulse modulation methods Pulse modulation replaces the continuous carrier with a regular train of pulses and varies one property of each pulse instead. In the analog members of this family, a pulse's amplitude, width, or position within its time slot carries the message value, giving pulse-amplitude, pulse-width, and pulse-position modulation respectively; each is the pulsed counterpart of amplitude or angle modulation, and each still transmits a continuous-valued message rather than a stream of bits. The digital members instead sample the message, round each sample to one of a finite set of levels, and transmit the result as a bitstream. [[Pulse-code_modulation|Pulse-code modulation]] sends the quantized value of every sample; [[Differential_pulse-code_modulation|differential pulse-code modulation]] sends only the difference between a sample and a value predicted from earlier ones, which is usually smaller and so needs fewer bits; [[Delta_modulation|delta modulation]] is the extreme case of this idea, encoding only the sign of that difference with a single bit per sample and relying on a high sampling rate to keep up with the message; and [[Delta-sigma_modulation|delta-sigma modulation]] pushes the sampling rate higher still, in exchange for needing very few bits per sample, which is why it is common inside modern [[Analog-to-digital_converter|analog-to-digital]] and [[Digital-to-analog_converter|digital-to-analog converters]] rather than as a transmission format in its own right. ## Miscellaneous modulation techniques A few techniques modulate a dimension outside amplitude, frequency, phase, and pulse timing. Spread-spectrum techniques deliberately spread a message's energy across a band far wider than the message itself needs, using a code the receiver also knows; the signal becomes harder to jam or intercept and, because many spread signals can share the same band with only a modest rise in each other's noise floor, several transmitters can be given the same frequency at once and separated again by their codes. Multicarrier techniques go the other way, splitting one wide channel into many narrow, mutually non-interfering subcarriers, each modulated at a low symbol rate, which tolerates a channel that behaves differently at different frequencies far better than a single wideband carrier does. Spatial modulation carries information in which antenna, or which combination of antennas, transmits, adding a fourth dimension of the carrier's state to the classical three; [[MIMO|multiple-input, multiple-output]] systems exploit the same multi-antenna freedom to send several independent streams through the same band at once rather than to encode one. Radar and sonar systems modulate a pulse's frequency linearly over its duration — a chirp — so that a long, low-power pulse can be compressed back into a short, high-resolution one after reception, a trick unrelated to carrying a message but built from the same frequency-varying idea as frequency modulation. ## Microsims The *Modulation* sketch puts one message signal through seven modulators at once and lets the reader compare them directly. The upper panel plots the message; the middle panel plots the modulated carrier, redrawn from scratch for whichever scheme is selected; the lower panel plots the magnitude spectrum, which is where the schemes look most different. Carrier frequency f_c (2–20 Hz) and message frequency f_m (0.1–3 Hz) set the two tones being combined; the modulation index β (0–1) sets how strongly the message acts on the carrier; and a selector switches the modulator among amplitude, frequency, phase, on-off keying, binary phase-shift keying, frequency-shift keying, and quadrature phase-shift keying. Live readouts give the Carson's-rule bandwidth for frequency modulation, the spectral efficiency in bits per second per hertz, and a power-efficiency figure in decibels. *Try:* Leave β and the two frequencies fixed and step the selector from amplitude to frequency modulation; watch the spectrum collapse from two clean sidebands into the wider, Bessel-weighted cascade of lines that the Carson's-rule bandwidth readout then reports. A three.js companion renders the carrier as a helix traced in in-phase, quadrature, and time coordinates, in which amplitude modulation breathes the helix's radius while frequency and phase modulation change how tightly it winds. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Signal_modulation) : [Wikitube](https://en.wikitube.io/wiki/Signal_modulation) Skeleton mirrored at revision 1365451036. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Amplitude_modulation]] - [[Frequency_modulation]] - [[Phase-shift_keying]] - [[Frequency-shift_keying]] - [[Amplitude-shift_keying]] - [[Carrier_wave]] - [[Analytic_signal]] ## References [^john021]: Johnson, D. *Fundamentals of Electrical Engineering I*. 2014, p. 21 (PDF page), Eq. 2.19: `A·cos(2π f0 t + φ) = Re[A·exp(jφ)·exp(j2π f0 t)]`. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 . CC BY. [^ell134]: Ellingson, S. *Radio Systems Engineering*, Revised 1st ed. 2023, pp. 133–134 (PDF pages): symbol alphabets of size *M*, log2 *M* bits per symbol, and Gray coding. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^ell149]: Ellingson, S. *Radio Systems Engineering*, Revised 1st ed. 2023, pp. 148–150 (PDF pages): coherent on-off keying versus binary phase-shift keying, and the noncoherent-detection penalty. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^ell158]: Ellingson, S. *Radio Systems Engineering*, Revised 1st ed. 2023, p. 158 (PDF page): incoherent *M*-ary frequency-shift keying's bit-error-rate bound improving as *M* grows. Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. *Citation needed:* a primary source (paper or patent) establishing priority and date for treating spatial/antenna selection as a formal fourth modulation dimension, as distinct from multiplexed multi-antenna transmission generally, is not yet pinned down here. ## Further reading - Steven Ellingson. *Radio Systems Engineering*, Revised 1st Edition (2023). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering - Christian Tiberius; Max Mulder. *Engineering Signal Analysis: From Fourier to filtering: Theory* (2026). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/engineering-signal-analysis-from-fourier-to-filtering-theory - Don Johnson. *Fundamentals of Electrical Engineering I* (2014). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/fundamentals-of-electrical-engineering-1 - Michael Stiber; Bilin Stiber; Eric Larson. *Signal Computing: Digital Signals in the Software Domain* (2020). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/signal-computing-digital-signals-in-the-software-domain ## External links - Live sketch: https://editor.p5js.org/sciencenibber/full/lmIXKnU4O - Editor source: https://editor.p5js.org/sciencenibber/sketches/lmIXKnU4O <!-- Hubs: Signal_processing. Portals: PORTAL_Signal_Processing. 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