Paley-Wiener Characterization of Kernels for Finite-Rate-of-Innovation Sampling

Mulleti, Satish and Seelamantula, Chandra Sekhar (2017) Paley-Wiener Characterization of Kernels for Finite-Rate-of-Innovation Sampling. In: IEEE TRANSACTIONS ON SIGNAL PROCESSING, 65 (22). pp. 5860-5872.

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Abstract

Exact reconstruction of finite-rate-of-innovation signals can be achieved by employing customized sampling kernels that satisfy certain frequency-domain properties. We impose compact support in time as an additional constraint. Considering frequency-domain reconstruction, we derive conditions for admissible sampling kernels and corresponding sampling rates. Our constructive kernel design methodology is based on the Paley-Wiener theorem for compactly supported functions. The new kernels satisfy generalized Strang-Fix conditions and have specific polynomial-modulated-exponential-reproducing properties. Unlike exponential splines, which have a support that is directly proportional to the number of exponentials they can generate, the proposed kernels have a support that is independent of that number. To analyze noise robustness, we consider a special member of the class that has a sum-of-modulated splines (SMS) form in the time domain and optimize its parameters to minimize the noise variance. The sum-of-sincs (SoS) kernel reported in the literature is an instance of this construction. In noise robustness analysis, SMS kernels show improvement in mean-squared error (MSE) compared with the state-of-the-art alternatives. In continuous-time noise, the improvement in MSE is about 2 dB for low signal-to-noise ratio (SNR) and 7 dB for high SNR. In the case of discrete white Gaussian noise, the MSE is lower by as much as 25 dB by using a higher-order SMS kernel compared with the SoS kernel for SNRs in the range of 10-15 dB.

Item Type:	Journal Article
Publication:	IEEE TRANSACTIONS ON SIGNAL PROCESSING
Additional Information:	Copy right for this article belongs to the IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 445 HOES LANE, PISCATAWAY, NJ 08855-4141 USA
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	13 Oct 2017 04:54
Last Modified:	13 Oct 2017 04:54
URI:	http://eprints.iisc.ac.in/id/eprint/57998

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