mponent. For a sampling frequency fs, various zones exist where, if a signal is band-limited to that zone, the original spectrum can be recov- ered. As shown in Fig. 5.20, at the sampling frequency fs, one can define zones where a band-limited signal in a higher Nyquist zone will alias down into the first Nyquist zone. For even-numbered Nyquist zones, the spectrum will appear in reversed order, and for odd-numbered zones, it appears in the original order. This means, for example, a 100 MHz band ranging from 700 to 800 MHz need only be sampled at 100 MHz to be characterized. As long as you know which Nyquist zone is occupied, you have all infor- mation to reconstruct the original signal. One issue is that the boundaries of the Nyquist zones are fundamentally tied to the sampling rate, which implies that the bandwidth of the desired signal must fit within a Nyquist zone. According to Poisson summation formula, 12 the samples of the Fourier transform of func- tion v(t) are sufficient to create a periodic extension of V(f) as V(f) = The latter equation can be interpreted as the sum of the replicas of V(f) shifted to integer multiples of fs (see Fig. 5.20). Fig. 5.20 also illustrates an example of the Nyquist frequency fs/2. Since these signals are repeated at multiples of fs, then for bandwidths greater than fs/2 aliasing and information loss will occur. The integer multiples of the Nyquist frequency determines the Nyquist Zones. In the literature, the Nyquist Zones are only defined for the positive frequency spectrum. In other words, the FFT of a discrete-time signal can be divided into an infinite number of fs/2 frequency bands, also known as Nyquist zones. The frequency spectrum between DC (zero frequency) and fs/2 is known as the first Nyquist zone. The frequency spectrum repeats itself over different Nyquist zones. Note that the even-numbered Nyquist zones appear as mirror images of the odd-numbered Nyquist zones. Aliasing in ADCs is a rami- fication of the sample-and-hold processing of the analog signal at the 