Editing Signal modulation (section)

===Fundamental digital modulation methods===
The most fundamental digital modulation techniques are based on [[keying (telecommunications)|keying]]:
* [[Phase-shift keying|PSK (phase-shift keying)]]: a finite number of phases are used.
* [[Frequency-shift keying|FSK (frequency-shift keying)]]: a finite number of frequencies are used.
* [[Amplitude-shift keying|ASK (amplitude-shift keying)]]: a finite number of amplitudes are used.
* [[Quadrature amplitude modulation|QAM (quadrature amplitude modulation)]]: a finite number of at least two phases and at least two amplitudes are used.

In QAM, an in-phase signal (or I, with one example being a cosine waveform) and a quadrature phase signal (or Q, with an example being a sine wave) are amplitude modulated with a finite number of amplitudes and then summed. It can be seen as a two-channel system, each channel using ASK. The resulting signal is equivalent to a combination of PSK and ASK.

In all of the above methods, each of these phases, frequencies or amplitudes are assigned a unique pattern of [[Binary numeral system|binary]] [[bit]]s. Usually, each phase, frequency or amplitude encodes an equal number of bits. This number of bits comprises the ''symbol'' that is represented by the particular phase, frequency or amplitude.

If the alphabet consists of <math>M = 2^N </math> alternative symbols, each symbol represents a message consisting of ''N'' bits. If the [[symbol rate]] (also known as the [[baud rate]]) is <math>f_{S}</math> symbols/second (or [[baud]]), the data rate is <math>N f_{S}</math> bit/second.

For example, with an alphabet consisting of 16 alternative symbols, each symbol represents 4 bits. Thus, the data rate is four times the baud rate.

In the case of PSK, ASK or QAM, where the carrier frequency of the modulated signal is constant, the modulation alphabet is often conveniently represented on a [[constellation diagram]], showing the amplitude of the I signal at the x-axis, and the amplitude of the Q signal at the y-axis, for each symbol.