Regularized Sampling of Multiband Signals

• Published in: IEEE transactions on signal processing Vol. 58; no. 11; pp. 5624 - 5638
• Main Author: Selva, J
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.11.2010; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analog to digital conversion; Analog-digital conversion, digital-analog conversion, pcm coding; Applied sciences; Approximation; Audio systems; cognitive radio; Exact sciences and technology; Frequency; Information, signal and communications theory; Linear systems; Low level; Mathematical analysis; Mathematical models; Miscellaneous; multiband sampling; Navigation; Noise level; Permission; Perturbation methods; Polynomials; Sampling; Sampling methods; Sampling, quantization; Signal and communications theory; signal interpolation; Signal processing; Signal sampling; spectrum-blind reconstruction; Studies; sub-Nyquist sampling; Synchronous; Telecommunications and information theory; Performance evaluation; signal interpolation; Trigonometric polynomial; Band limited signal; Infinite medium; cognitive radio; Audio systems; spectrum-blind reconstruction; Time interval; Sampling; Analog to digital conversion; sub-Nyquist sampling; Navigation system; AD conversion; Subspace method; Multirate system; Perturbation; Periodic signal; multiband sampling; Interpolation; Linear system; Telecommunication system; Signal processing; Numerical simulation; Software radio
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2010.2057248

This paper presents a regularized sampling method for multiband signals, that makes it possible to approach the Landau limit, while keeping the sensitivity to noise and perturbations at a low level. The method is based on band-limited windowing, followed by trigonometric approximation in consecutive time intervals. The key point is that the trigonometric approximation "inherits" the multiband property, that is, its coefficients are formed by bursts of elements corresponding to the multiband components. It is shown that this method can be well combined with the recently proposed synchronous multirate sampling (SMRS) scheme, given that the resulting linear system is sparse and formed by ones and zeroes. The proposed method allows one to trade sampling efficiency for noise sensitivity, and is specially well suited for bounded signals with unbounded energy like those in communications, navigation, audio systems, etc. Besides, it is also applicable to finite energy signals and periodic band-limited signals (trigonometric polynomials). The paper includes a subspace method for blindly estimating the support of the multiband signal as well as its components, and the results are validated through several numerical examples.