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Each of these is appropriate in certain situations.

For the first case, consider [link] , which shows the spectrum of the FDM signal priorto downconversion. Let f 3 + f * be the frequency of the upper edge of the user spectrum near the carrier at f 3 . By the Nyquist principle, the upconvertedreceived signal must be sampled at a rate of at least 2 ( f 3 + f * ) to avoid aliasing. For high frequency carriers, this exceeds the rateof reasonably priced A/D samplers. Thus directly sampling the received signal (and performing all the downconversiondigitally) may not feasible, even though it appears desirable for a fully software based receiver.

In the second case, the downconversion (and subsequent lowpass filtering) are done in analog circuitry,and the samples are taken at the output of the lowpass filter.Sampling can take place at a rate twice the highest frequency f * in the baseband, which is considerably smaller than twice f 3 + f * . Since the downconversion must be done accurately in orderto have the shifted spectra of the desired user line up exactly (and overlap correctly),the analog circuitry must be quite accurate. This, too, can be expensive.

In the third case, the downconversion in done in two steps: an analog circuit downconverts to some intermediate frequency, where thesignal is sampled. The resulting signal is then digitally downconverted to baseband. The advantageof this (seemingly redundant) method is that the analog downconversion can be performed with minimalprecision (and hence inexpensively), while the sampling can be done at a reasonable rate (and hence inexpensively).In [link] , the frequency f I of the intermediate downconversion is chosen to be large enoughso that the whole FDM band is moved below the upshifted portion. Also, f I is chosen to be small enough so that the downshifted positive frequency portion lower edge does not reach zero.An analog bandpass filter extracts the whole FDM band at an intermediate frequency (IF), and then it is onlynecessary to sample at a rate greater than 2 ( f 3 + f * - f I ) .

Downconversion to an intermediate frequency is common since the analog circuitry can be fixed, and the tuning(when the receiver chooses between users) can be done digitally. This is advantageous since tunable analog circuitryis considerably more expensive than tunable digital circuitry.

FDM downconversion to an intermediate frequency
FDM downconversion to an intermediate frequency

Digital communications around an analog core

The discussion so far in this chapter has concentrated on the classical core of telecommunication systems:the transmission and reception of analog waveforms.In digital systems, as considered in the previous chapter, the original signal consists of a stream of data,and the goal is to send the data from one location to another. The data may be a computer program, ASCII text,pixels of a picture, a digitized MP3 file, or sampled speech from a cell phone. “Data” consist of a sequence ofnumbers, which can always be converted to a sequence of zeros and ones, called bits . How can a sequence of bits be transmitted?

The basic idea is that, since transmission media (such as air, phone lines, the ocean) are analog, thebits are converted into an analog signal. Then this analog signal can be transmittedexactly as before. Thus at the core of every “digital” communication system lies an “analog” system.The output of the transmitter, the transmission medium, and the front end of the receiver are necessarily analog.

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Source:  OpenStax, Software receiver design. OpenStax CNX. Aug 13, 2013 Download for free at http://cnx.org/content/col11510/1.3
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