The Bandpass Sampling Theorem

In all sampled systems, the signal must be band-limited before it is sampled. Our 2^nd i.f. signal already is. On the other hand, it is not centred at zero frequency, that is, it is not a baseband signal but a band-pass signal, and so it is not immediately obvious which sampling rate will be required to represent it correctly.

We will figure this out by applying the bandpass sampling theorem, which states that:

a signal of bandwidth B, occupying the frequency range between f_L and f_L + B, can be uniquely reconstructed from the samples if sampled at a rate f_S :

f_S >= 2 * [1 + (f_L/B)] B / (M+1)

where

M = int (f_L/B)

In the EISCAT UHF and VHF receivers,

f_L =8.3 MHz
B =6.4 MHz

leading to f_S >= 2 * [1 + (8.3/6.4)]*6.4 / [int (8.3/6.4) + 1] = 14.7 MHz

Clocking the A/D at 15.000 MHz will therefore result in the (8.3 - 14.7) MHz 2^nd i.f.signal being correctly sampled, with some margin. This is certainly not a coincidence; during the system design phase, the bandpass sampling theorem was used in reverse to find the maximum allowable anti-aliasing filter bandwidth, given a 15.000 MHz sampling rate and realistic filter performance !

References:

Kohlenberg, A., Exact interpolation of band-limited functions, J. Appl. Phys., 24(12), 1432-1436, 1953.

Peebles, P. Z., Jr., Communications Systems Principles, pp. 305-306, Addison-Wesley, Reading, Mass. 1976.