0.4 Analog (de)modulation

Beam me up, Scotty.

—attributed to James T. Kirk, Starship Enterprise , “Star Trek”

Several parts of a communication system modulate the signal and change the underlyingfrequency band in which the signal lies. These frequency changes must be reversible; after processing, the receiver must beable to reconstruct (a close approximation to) the transmitted signal.

The input message $w\left(kT\right)$ in [link] is a discrete-time sequence drawn from a finite alphabet.The ultimate output $m\left(kT\right)$ produced by the decision device (or quantizer) is also discrete-time and is drawnfrom the same alphabet. If all goes well and the message is transmitted, received,and decoded successfully, then the output should be the same as the input,although there may be some delay $\delta$ between the time of transmission and the time when theoutput is available. Though the system is digital in terms of the message communicatedand the performance assessment, the middle of the system is inherently analog from the (pulse-shaping)filter of the transmitter to the sampler at the receiver.

At the transmitter in [link] , the digital message has alreadybeen turned into an analog signal by the pulse shaping (whichwas discussed briefly in [link] and is considered in detail in [link] ). For efficient transmission, the analog version of the messagemust be shifted in frequency, and this process of changing frequencies is called modulation or upconversion.At the receiver, the frequency must be shifted back down, and this is called demodulation or downconversion.Sometimes the demodulation is done in one step (all analog) and sometimes the demodulation proceeds in twosteps; an analog downconversion to the intermediate frequency and then a digital downconversion to thebaseband. This two step procedure is shown in [link] .

There are many ways that signals can be modulated. Perhaps the simplest is amplitude modulation , which is discussed in two forms (large and small carrier) in the nexttwo sections. This is generalized to the simultaneous transmission of twosignals using quadrature modulation in "Quadrature Modulation" , and it is shown that quadrature modulation uses bandwidth more efficiently than amplitude modulation.This gain in efficiency can also be obtained using single sideband and vestigial sideband methods, which are discussed in the document titled Other Modulations , available on the website.Demodulation can also be accomplished using sampling as discussed in [link] , and amplitude modulation can also be accomplished witha simple squaring and filtering operation as in Exercise  [link] .

Throughout, the chapter contains a series of exercises that prepare readers to create their own modulationand demodulation routines in M atlab . These lie at the heart of the software receiver that will beassembled in [link] and [link] .