Modulation is a process where a baseband signal is converted into a radio frequency (RF) signal. Demodulation is an inverse process, where the baseband signal is recovered from the RF signal. An RF signal has two degrees of freedom, namely, amplitude and phase, or in-phase and quadrature components. Modulation is carried out by varying these components according to the baseband signal. Digital modulation is different from analog in the sense that the digital signal takes finite discrete levels. Due to this feature, some particular techniques can be applied to the modulation and demodulation in digital communications.

The requirements for digital modulation are the following: narrow bandwidth of the modulated signal, low bit error rate, and easy implementation of the modulation/demodulation circuits.

This section describes briefly some general topics of digital modulation and demodulation. The reader may refer many books [1–8] for further details.

A modulated signal can be expressed generally as

where *A*(*t*) is the amplitude of the envelope, *φ*(*t*) the phase, *ω*
_{c} the (angular) frequency of the carrier signal, and
, the complex baseband signal. We can rewrite the above equation as

where *x*(*t*) = *A*(*t*)cos*φ*

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