  A new segmented compressed sampling method for analog-to-information
conversion (AIC) is proposed. An analog signal measured by a number of parallel
branches of mixers and integrators (BMIs), each characterized by a specific
random sampling waveform, is first segmented in time into $M$ segments. Then
the sub-samples collected on different segments and different BMIs are reused
so that a larger number of samples than the number of BMIs is collected. This
technique is shown to be equivalent to extending the measurement matrix, which
consists of the BMI sampling waveforms, by adding new rows without actually
increasing the number of BMIs. We prove that the extended measurement matrix
satisfies the restricted isometry property with overwhelming probability if the
original measurement matrix of BMI sampling waveforms satisfies it. We also
show that the signal recovery performance can be improved significantly if our
segmented AIC is used for sampling instead of the conventional AIC. Simulation
results verify the effectiveness of the proposed segmented compressed sampling
method and the validity of our theoretical studies.
