Digital Receiver Handbook: Basics of Software Radio

Digital Receiver Handbook: Basics of Software RadioTheory of OperationDigital Receiver Block DiagramAliasingFigure 3 Figure 4Take a look at the digital receiver block diagramshown in Figure 3. Note the strong similarity to theanalog receiver diagram—all of the basic principles ofanalog receivers still apply.Right after the RF amplifier and an optional RFtranslator stage, we use an A/D (analog-to-digital)converter to digitize the RF input into digital samplesfor the subsequent mixing, filtering and demodulationthat are performed using digital signal processingelements.Before we continue, lets first review a theoremfundamental to sampled data which lays the foundationfor the A/D converter requirements.Nyquist’s Theorem:“Any signal can be represented by discrete samplesif the sampling rate is at least twice the bandwidth of thesignal.”For example, if we use an A/D converter samplingat 70 MHz, then the bandwidth of the analog inputmust be less than 35 MHz.Now let’s see what happens if we ignore Nyquist’scriterion.Figure 4 shows a frequency display of a systembeing sampled at frequency fs. For all input signalsbelow fs/2, such as the one at fo, we fully meet theNyquist criterion. In fact, any number of signals can bepresent in the shaded region and all will be correctlyrepresented in the sampled data.But if we have a signal present at say, fa, which isabove fs/2, the sampling process will generate an aliasedimage which will appear in the sampled data at fs - fa.This image cannot be distinguished from a true signalwhich might have been present at that same frequency.The point is this: once an aliased image is created inthe sampling process, no amount of further processingcan distinguish between a true signal and an aliasedsignal. Therefore, it is imperative to prevent aliasingbefore it occurs.4Pentek, Inc. • One Park Way, Upper Saddle River, NJ 07458 • Tel: (201) 818-5900 • Fax: (201) 818-5904 • Email: digrec@pentek.com • http://www.pentek.com