Sub-Nyquist sampling of multiband signals: perfect reconstruction and bounds on aliasing error

We consider the problem of periodic nonuniform sampling of a multiband signal and its reconstruction from the samples. We derive the conditions for exact reconstruction and find an explicit reconstruction formula. Key features of this method are that the sampling rate can be made arbitrarily close to the minimum (Landau) rate and that it can handle classes of multiband signals that are not packable. We compute various bounds on the aliasing error due to mismodeling the spectral support and examine the performance in the presence of additive white sample noise. Finally we provide optimal designs for the reconstruction system.