The demodulation of a passband waveform or of a complex baseband waveform uses methods similar to those used to demodulate baseband signals. However, there are many new details that emerge in the larger setting of passband or complex baseband demodulation. This is because a complex baseband function (or a passband function) can be expressed either in terms of real and imaginary components or in terms of amplitude and phase. It is obvious that phase is meaningful only if there is an absolute phase reference. A new set of topics arises when the modulator and demodulator do not share a common phase reference. This is the distinction between coherent and noncoherent demodulation. When the phase reference is known to the demodulator, the demodulator is called a coherent demodulator. When the phase reference is not known to the demodulator, that demodulator is called a noncoherent demodulator.

We begin the chapter with a study of the matched filter at passband. Then we use the matched filter as a central component in the development of a variety of demodulators, both coherent and noncoherent, for the passband waveforms that were introduced in Chapter 5.

The methods for the demodulation of baseband sequences that were described in Chapter 4 can be restated in the setting of passband waveforms. We shall prefer, however, the equivalent formulation in terms of complex baseband waveforms. It becomes obvious immediately how to generalize methods of demodulation from sequences of real numbers to sequences of complex numbers, so the chapter starts out with a straightforward reformulation of the topic of demodulation.