Direct sampling and demodulation of carrier-frequency signals

We show that a generalized carrier-frequency signal can be directly and efficiently coarse-sampled based upon the notion of the space-bandwidth product. Using an envelope function form, we treat both amplitude-modulation and frequency-modulation cases simultaneously. We derive exact formulas for the sampled carrier-frequency signal and for the sampled envelope, showing that it is possible to recover the envelope from the coarsely sampled carrier without conventional mixing or heterodyning. This alternative to the conventional demodulation methods is illustrated with numerical examples including phase retrieval. Extension to the two-dimensional case is also included. (C) 2002 Elsevier Science B.V. All rights reserved.