Acquisition of multiband signals with minimum sub-Nyquist sampling

It is widely known that signals with sparse spectrums may be properly acquired when using specific sub-Nyquist sampling frequencies. This alleviates the sampling requirements in advanced acquisition systems, such as the direct-sampling solution to the software-defined radio paradigm. Unfortunately, beyond the theorem of bandpass sampling, analytical expressions for these valid sub-sampling rates are unavailable. Previously, the authors derived the analytical rules which guarantee that the minimum sub-Nyquist sampling frequency avoids aliasing. However, these equations are only valid for the restricted case of evenly-spaced equal-bandwidth multichannel systems, being useless in a broader framework with arbitrary-bandwidth channels. In this work, the general dual-band case is exhaustively analyzed. Given the channel bandwidths, the spectrum parameters which assure that the minimum sub-Nyquist frequency does not give rise to aliasing may be found. For more-than-two channels, some simple guidelines are also provided. Finally, simulation examples are shown to confirm the correctness of the deduced equations.