Compressive Sensing of Analog Signals Using Discrete Prolate Spheroidal Sequences

Compressive sensing (CS) has recently emerged as a framework for efficiently capturing signals that are sparse or compressible in an appropriate basis. While often motivated as an alternative to Nyquist-rate sampling, there remains a gap between the discrete, finite-dimensional CS framework and the problem of acquiring a continuous-time signal. In this paper, we attempt to bridge this gap by exploiting the Discrete Prolate Spheroidal Sequences (DPSS's), a collection of functions that trace back to the seminal work by Slepian, Landau, and Pollack on the effects of time-limiting and bandlimiting operations. DPSS's form a highly efficient basis for sampled bandlimited functions; by modulating and merging DPSS bases, we obtain a dictionary that offers high-quality sparse approximations for most sampled multiband signals. This multiband modulated DPSS dictionary can be readily incorporated into the CS framework. We provide theoretical guarantees and practical insight into the use of this dictionary for recovery of sampled multiband signals from compressive measurements

A Multitaper-Random Demodulator Model for Narrowband Compressive Spectral Estimation

The random demodulator (RD) is a compressive sensing (CS) system for acquiring and recovering bandlimited sparse signals, which are approximated by multi-tones. Signal recovery employs the discrete Fourier transform based periodogram, though due to bias and variance constraints, it is an inconsistent spectral estimator. This paper presents a Multitaper RD (MT-RD) architecture for compressive spectrum estimation, which exploits the inherent advantage of the MT spectral estimation method from the spectral leakage perspective. Experimental results for sparse, narrowband signals corroborate that the MT-RD model enhances sparsity so affording superior CS performance compared with the original RD system in terms of both lower power spectrum leakage and improved input noise robustness