  Because optical systems have huge bandwidth and are capable of generating low
noise short pulses they are ideal for undersampling multi-band signals that are
located within a very broad frequency range. In this paper we propose a new
scheme for reconstructing multi-band signals that occupy a small part of a
given broad frequency range under the constraint of a small number of sampling
channels. The scheme, which we call multi-rate sampling (MRS), entails
gathering samples at several different rates whose sum is significantly lower
than the Nyquist sampling rate. The number of channels does not depend on any
characteristics of a signal. In order to be implemented with simplified
hardware, the reconstruction method does not rely on the synchronization
between different sampling channels. Also, because the method does not solve a
system of linear equations, it avoids one source of lack of robustness of
previously published undersampling schemes. Our simulations indicate that our
MRS scheme is robust both to different signal types and to relatively high
noise levels. The scheme can be implemented easily with optical sampling
systems.
