  Multi-Coset (MC) sampling is a well established, practically feasible scheme
for sampling multiband analog signals below the Nyquist rate. MC sampling has
gained renewed interest in the Compressive Sensing (CS) community, due partly
to the fact that in the frequency domain, MC sampling bears a strong
resemblance to other sub-Nyquist CS acquisition protocols. In this paper, we
consider MC sampling of analog frequency hopping signals, which can be viewed
as multiband signals with changing band positions. This nonstationarity
motivates our consideration of a segment-based reconstruction framework, in
which the sample stream is broken into short segments for reconstruction. In
contrast, previous works focusing on the reconstruction of multiband signals
have used a segment-less reconstruction framework such as the modified MUSIC
algorithm. We outline the challenges associated with segment-based recovery of
frequency hopping signals from MC samples, and we explain how these challenges
can be addressed using conventional CS recovery techniques. We also demonstrate
the utility of the Discrete Prolate Spheroidal Sequences (DPSS's) as an
efficient dictionary for reducing the computational complexity of segment-based
reconstruction.
