The Use of Discrete Prolate Spheroidal Sequences and Trig Prolates to Compressed Sensing

Compressed sensing may offer the possibility to acquire certain signals at a rate below Nyquist with guaranteed perfect recovery of these signals. In the present article, we investigate the utilization of Discrete Prolate Spheroidal Sequences as a sparsifying basis for multiband signals, from where compressed sensing may be applied. We also compare their use with the use of trig prolates, a similar and simpler to compute basis, in the context of compressed sensing. Using CoSaMP as the reconstruction algorithm we demonstrate the infeasibility of trig prolates as a basis for perfect recovery.