The sampling theorem, as we have derived it, states that a signal x(t) must be us sample...

The sampling theorem, as we have derived it, states that a signal x(t) must be us sampled at a rate greater than its bandwidth (or equivalently, a rate greater than twice its highest frequency). This implies that if x(t) has a spectrum as indicated in figure P7.26(a) then x(t) must be sampled at a rate greater than . However, since the signal has most of its energy concentrated in a narrow band, it would seem reasonable to expect that a sampling rate lower than twice the highest frequency could be used. A signal whose energy is concentrated in a frequency band is often referred to as a bandpass signal. There are a variety of techniques for sampling such signals, generally referred to as bandpass-sampling techniques.

To examine the possibility of sampling a bandpass signal as a rate less than the total bandwidth, consider the system shown in Figure P7.26(b). Assuming that , find the maximum value of T and the values of the constants A, , and such that .